I'll try to answer your question, sorry if it doesn't satisfy you. I've previously addressed the Ottoman immigration to America here

There could be a lot of ways. First is by word of mouth from an American, which can be commonly found in American missionary schools. The Tanzimat education reforms in 1839 led to the support of Ottoman government for foreign, especially American missionary schools. It was a sincere effort of the government because it supported them, despite the fact that they benefited only Christians and sometimes became recruiting centers for separatist movements. Because it's primarily a missionary school, the teachers were also looking for people to convert. Jews, Muslims, and Orthodox Christians generally refused to convert, but Armenians often willingly convert in large numbers despite strong opposition from Armenian Gregorian Church. American missionaries then sponsored Armenian students in America and then promoted Armenian migration to the United States. The American missionaries portray America as a land free from any omnipotent ruler with liberty, democracy, and equality. As a result, Armenians began migrating to America in large numbers. For example, when the Harput consulate (the missionary school had already been operated by 1855) opened in 1910 there were 260 Armenians who had become American citizens and the numbers increased by year. Eventually the Turks joined the Armenians migrating to the United States, mostly for the prospect of wealth. Topheliyan, an Armenian immigrant wrote in 1892 that American missionaries deceived some Muslims in Anatolia by promising them a job, made them migrate and then converted them to Christians. Ottoman officials tried to restrict this uncontrolled migration but failed, and immigrants from Harput reached 3000 per year (though this number is quite unreliable)

Second and the most prominent way is from stories. Successful emigrants who returned home from the Americas with considerable wealth, including money to build large houses, and with their tales about the riches and availability of employment fueled a chain migration of other family members or residents from their home villages, even those who had money were tempted to move to the Americas in search of better opportunities and wealth. It was evident considering the Muslim Turks who migrated to the United States were mainly from the villages and small towns like Dersim, Malatya, Rize, Samsun, and the like. Stories of opportunity in America could easily have spread among the communities of these towns and villages. The United States, usually referred to as 'Amrika' in these stories represent hope, the possibility of achieving the impossible, instant wealth, economic security and relief from a life of abject poverty. Another way on this stories were told is by letters. Letters to families, relatives and friends telling them about the job opportunities and riches in the United States provided important information about the Americas, such as the routes to travel and the preferred shipping lines. Within a year many such immigrants were able to send a prepaid tickets to the family. The stories told in the letters sent home did not take long to reach the other communties of the region. This then resulted in a chain of migration among all the Ottoman citizens. For example, A Turkish laborer in Peabody told in an interview:

Most of us are from Harput. There are also Turks from Sivas, Malatya and Elazığ among us ... We observed that Armenians from our homeland were going to the United States for commerce. We thought we could also try commerce because we were in trouble at that time. As soon as the newcomers found jobs, they invited the relatives and friends. And Turkish society became larger day by day

An Armenian Sabiha Sertel also recounts a similar thing:

Armenians, who went to the United States and then came back, told that everybody in the United States became rich and it was easy to find jobs there. When they were going to the United States again, they persuaded many Turks to come with them. Some of the Turks decided to migrate because of the letters they received from their friends in the United States

And most of these immigrant Turks often ended up successful, thanks to the extensive network of Ottoman workers that helped their friends, family, and relatives in looking jobs and livelihood. The established migrant then tell their friends and relatives back home, and so forth

Lastly is by advertisements. American industries, steamship companies, and railroads often advertised overseas to Ottoman citizens for potential workers, promising excellent working conditions and wages. Moreover, there were various immigrant groups and press that functioned as employment agencies. For example, Bedros Torosian tried to attract his fellow Armenians and urged them to settle in New Jersey which was "attractive, clean, and healthy" and wanted Armenian laborers to work there. Steamship companies, drawn by the prospect of lucrative transportation business also advertised immigration the America. The tales of shipping agents about the riches of America encouraged many Ottomans to leave for the United States, advertising the safety and comfort of their vessels or even admitting immigrants without passports to obtain foreign ones later. They eventually became the most successful travel agents for Turkish immigration beginning in the second half of the 19th century

Sources/Bibliography:

The Ottoman Emigration to America, 1860-1914 by Kemal Karpat

Outposts of an Empire: Early Turkish Migration to Peabody, Massachusetts by Işıl Acehan

Turks in America: The Ottoman Turk’s Immgrant Experience by Frank Ahmed