Lincoln did have the reputation of being a tyrant. Both in the north and south.

In the north some anti-war Democrats viewed Lincoln as a tyrant for engaging in a costly war. These Democrats were called "Copperheads", named after venomous snakes. They were named Copperheads because many in the north viewed them as a danger to the war effort.

Other people in the north viewed Lincoln as a tyrant not because of the war, but because of the consolidation of power in the executive branch. Lincoln did exercise a lot power. Without approval from Congress he order military blockades and spent a large amount of funds. Lincoln also suspend civil liberties like habeas corpus.

But the Confederacy viewed Lincoln as a provoker of war more so than a tyrant. Both during and after the conflict the Confederacy claimed Lincoln induced an unnecessary war on the Confederacy.

Jefferson Davis argued the legal and moral legitimacy of the formation of a separate nation. Davis claimed the southern government wanted to reach an agreement concerning the fate Fort Sumter (and other forts) but was forced to react military due to Lincoln sending "a hostile fleet" towards South Carolina and Fort Sumter.

Many Confederate citizens viewed Lincoln as a tyrant. But the prevailing narrative during the civil war was Lincoln as a provoker of war. Hence the inflammatory term the "war of northern aggression".

Actually, there is no certainty to what he exactly said. If you think about the pandemonium and how our brains fill in information during and after events, and if you remember there were no recording devices, we not have a 100% understanding of what Booth said.

What I am about to share below I've paraphrased from a terrific book that I am sure you will love: "We Saw Lincoln Shot: One Hundred Eyewitness Accounts" by Timothy S. Good.

Some witness say he said "Sic Semper Tyrannis". Others say it was only "Sic Semper". Some heard "The South shall be free", while some distinctly heard the word "Freedom". Two witnesses claim he said "Revenge for the South", another heard "The South is avenged!" Two others heard "I have done it". Another witness said Booth said nothing at all.

I should add though that Booth himself in his diary stated that he shouted "Sic semper", not "Sic Semper Tyrannis". source

Btw, "Sic Semper Tyrannis" was/is the State motto of Virginia.