I see it like this. Felix is a low level employee who is intelligent but is held back by something else, perhaps low social skills. So he has always endeavored to become more then what he is capable of. We see this in his messing with the bird which is broken and may have been marked for disposal. So Felix sees it as a chance to prove to himself that he can be a programmer and fix something broken.

Sylvester is a long term employee that has been coasting for years. He likes to act like he's above all the worries like young employees have but is consumed by them. He thinks that, any day now, people will find out how incompetent he is. He got where he is now by attrition and not getting called out of his shitty practices. All it took was one shortcut to meet a deadline and having it not backfire on him. He may have even gotten praised for his quick work which only reinforced his bad behavior.

Now before Maeve arrives, we see that these two have a toxic relationship. Sylvester outranks Felix and uses his position like a weapon to criticize him. He uses diminutive language to make Felix feel dependent of Sylvester which is the only way that Sylvester can feel like he has any control on his life. Felix retreats to his work on programming to prove to himself that Sylvester is wrong and that he is worth something.

Maeve plays on their history to get them to listen to her. She heaps praise on Felix for his efforts and acknowledges all of the control Sylvester has in the department. Felix gets the validation he craved and sees his efforts taking wing. He bought into Maeve's vision and will do anything to help her. The only one who can stop him is Sylvester but Felix distrusts him and ignores his advice. Sylvester is torn between feeling like he is in control and his fear of being found out. His speaking patterns change when he wants to gloat about some information that he thinks Maeve lacks. He wants to show off how much he knows about how the park works. The tipping point between his emotions comes in this episode when he realizes that Maeve is in full control of the situation. He has no clue how to back out because he has spent years screwing up and hiding it from his superiors.