Someone who pushes someone else's buttons: someone who goads, annoys, provokes, etc.
When you're dealing with Tom, you need to keep in mind that he can be a button pusher sometimes. Stay cool, and don't reinforce that behavior.
A low-skilled or unskilled worker: someone from whom one can expect little or nothing more than rote pushing of buttons (not showing, for example, critical thinking, insight, or leadership).
Bill has been working here for 4 years and is looking for ways to upskill. He says he doesn't want to be a button pusher forever.