Edit: I am also going to briefly preface this by saying that I am Cuban American and I support normalization.

Why do Cuban-Americans dislike the Castro administration? Do they dislike them for the same reasons as the US government?

The reasons are as many as the Cuban Americans themselves. It really depends on their individual experiences, which are further conditioned by what wave of immigrants they formed a part of.

The initial wave, relatively small, was just people connected to the Batista regime who were fleeing possible reprisals. Because their property may have been connected to corrupt sources or have been directly based on the criminal policies of the Batista regime, these people usually lost everything due to expropriations.

A second wave, much larger, was from between 1959 and 1961, made up of individuals who either a) owned property that was being expropriated (land, large businesses, etc.) or b) had firm ideological reasons to fear Communism (Conservative Catholics for example). A lot of these individuals were white and from comfortably middle to upper class backgrounds. Many felt betrayed because Fidel had promised numerous times that the Revolution would be 'Green like the palm trees and never Red', and yet the Revolution was every day more openly Socialistic and the expropriations of wealth more far reaching.

The third major wave of immigrants was during the 1980 Mariel Boatlift and was very different in composition. These were people who had lived under the Castro regime but were either unsatisfied with the standard of living or, more importantly, politically disaffected. Between 1965-1968 the UMAP forced labor camps were created to reeducate those sent to them through hard labor (and with the sign 'Work will make you Men' above the entrance). The camps were closed down after international outcry, but during their brief existence they were the place that homosexuals (who weren't considered 'real men'), 'hippies', and other people considered a-social or politically disaffected individuals were sent. Homosexuals who feared being targeted to be sent to the camps slept on the floor of Guillermo Cabrera Infante's home, because as he was the editor for a major Cuban magazine they hoped he could offer them protection.

In 1968 the Great Revolutionary Offensive happened, in which all remaining private business was nationalized. From then on all work (aside from the peasants who still held land from the land reform and refused to join State run cooperatives) had to be for the State. Nationalizations went beyond simply going after big business and now included barber shops, shoeshine stands, and any other small business.

In the cultural world, the "Words to the Intellectuals" that Fidel had spoken at the beginning of the 1960s ("Within the Revolution all is permitted; outside of the Revolution, nothing") began to be implemented. The infamous Padilla Affair evolved between 1968 and 1970, in which Heberto Padilla was first chastised by the writer and artist union (UNEAC) for the 'ideological' and political implications of his book, ended with his arrest (over rumors of writing a supposedly subversive book) and later his liberation only to culminate in his public breakdown where he accused other writers of harboring similar anti-government sympathies and confessed his political sins.

The 1971 Congress on Culture and Education marked the beginning of open Sovietization, with policies like preventing foreign clothing styles from entering the country (due to its potential pernicious bourgeois influence) to the prohibition of homosexuals from being able to obtain positions in which they could influence and 'recruit' they youth. These are still codified and written for all to see in the pamphlet created at the end of the Congress. [Edit: Just to be clear, these policies were rolled back and Cuba currently has a pretty advanced policy when it comes to LGBT issues. These reforms are due in large part to the influential efforts of Raul Castro's daughter, Mariela Castro, whose family connection protected her and offered her the platform she needed to get through the difficult initial push]

Culture increasingly became a utilitarian arm of the State, leading to an explosion of works of fiction with little literary quality but solid pro-government values, with writers and artists like Padilla, Anton Arrufat, and others, sidelined.

The government by then had done away with all but the more superficial trappings of bourgeois democratic controls, centralizing the economic, social, and political life of the country in the hands of the Central Committee of the Communist Party, which was essentially synonymous with Fidel at this point.

This caused pressure and discontent to build up until the Mariel Boatlift in 1980, when Fidel allowed all who would like to leave safe passage to the port of Mariel where they could be picked up by family or humanitarians from the US. The government organized "acts of repudiation" against those who left, in which neighbors would (usually at the direction of government agents) gather around the home of someone preparing to leave, throw eggs at the house and yell things like escoria! (trash)

Many marielitos (those who left during Mariel) never forgave the government.

The immigrant crisis of the 1990s was more economic than political and was one of the most racially diverse. People were hungry and tired of living in the post-1991 economic crisis which made life in Cuba a living hell. Irregular water, electricity, gas, etc. Food was difficult to obtain at any price. The government called it the "Special Period". Whatever it is called, it left the population severely traumatized, many having been forced to do extremely difficult (not always ethical) things just to survive.

The post-1990s immigrants are also largely economic immigrants, with some political immigrants mixed in thanks to sporadic repression, like the "Black Spring" in 2003 when the government rounded up politically subversive media (often with very real links to the US) and put them in jail.

There are more reasons than this but it should give you a brief idea of their grievances.

What made Cubans think change was happening for the worse (assuming they planned on leaving)?

Depends on the moment they left. Each and every one had a moment or issue which began to change their view on the positive-negative direction the country was going.

A lot of good was done during this period. Illiteracy was effectively wiped out, education was made accessible to whole of the country regardless of income, healthcare was made available everyone, etc. But the good didn't outweigh the bad for many, including supporters of the government.

Why did USA support Batista (a dictator), then not support Castro (a dictator)? Issues from the Cold War aside, is there any other reasons? Or is that it?

The US supported Batista like it supported other Latin American dictators back then; if you could keep 'order' (prevent uprisings that endangered American lives or property) and were willing to make concessions to American business interests, the US government was fine with supporting you. We were also supporting Rafael Leonidas Trujillo during the 50s, despite him ordering the massacre by machete of thousands of Haitian immigrants or running one of the most chilling political regimes in the Americas at the time. In 1954 the US overthrew the democratically elected constitutional government of Guatemala for mere land reforms, installing a military regime that promised not to threaten the business interests of the United Fruit Company or other American corporations.

Is it true people left because of the redistribution of wealth? Is it more complicated than?

Some definitely did. Especially the second wave, made up largely of people whose wealth was being expropriated. But as you can see, there were numerous legitimate reasons to leave.

Sources:

-María del Pilar Díaz Castañón: Ideologia y Revolucion: Cuba 1959-1962. Editorial de Ciencias Sociales, 2001.

-Lars Schoultz: That Infernal Little Cuban Republic: The United States and the Cuban Revolution Book, UNC Press, 2011.

-Documentary: Conducta Impropia, 1984. [Use this one carefully as it is a politicized documentary with a clear objective, however it remains useful for its interviews with those who fled Cuba during the Mariel Boatlift]

-Felix Masud-Piloto: With Open Arms: The Evolution of Cuban Migration to the U.S., 1959-1995, Rowman & Littlefield Publishers.

-Copy of the "Speech to the Intellectuals" Fidel gave in the early 1960s which marked the beginning of a chill between the government on the one hand and writers and artists on the other: http://lanic.utexas.edu/project/castro/db/1961/19610630.html

-Louis Perez Jr.: Cuba Between Reform and Revolution, Oxford University Press (now on its 4th edition).