Usually the events were cutscenes or QTEs (timed button presses) that you either pass or get a gameover if you fail too many.
Now this wouldn't be an issue if the games were marketed as such but instead they tried to present them with the taglines "Your choices have consequences" while it was clearly not the case. You could run the same game twice making completely opposite choices and the end results were always the same; sometimes a character would die but at most that just resulted in some extra dialogue since those characters were designed to be non essential.
Here is an example of what I mean: Alice is a fugitive on the run and needs a car so she can:
1)Go to her friend Bob and have him drive the car after asking him 2)Threaten Bob to drive her around
In the end Bob is always driving the car and his opinion of you doesn't matter outside a throwaway line where he says "Hey, you owe me!" or "Hey, you're a jerk!"
The illusion of choice is very apparent at times even DURING the game since the events occurring are just too limiting.
It didn't help that Life is Strange and the Witcher 3 came out and had more in depth consequences and exploration of these systems.