The NFL requires an official to be at their position for 5 years before they can work the playoffs.
The NBA has a similar year requirement before they can work the playoffs.
I am pretty sure that MLB has a requirement.
I have no idea about NHL, nor do I care what their requirements are.
After these officials have reached the required number of years under your belt, yes what you do during the season will affect assignments. The NFL has a "playoff type" system with their officials. Everyone starts out in the playoffs at the same level and based on how they do in each game they can advance to the next round. I do not know what the NBA does or MLB does, but I know MLB umpires that work the Championship series might not at all work the World Series. Someone can work the World Series and not work the ALCS or the NLCS from what I understand.
Peace