It is a "push". The other answers are overthinking this way too much. If you push off of someone you are pushing someone which is a foul.
Here are the types of fouls in basketball (ALL OF THEM):
- Blocking
- Holding
- Hand Check
- Push (Charging)
- Illegal use of hand (not really called because the foul usually hits another category)
- Player control.
Those are all the foul categories a player can commit. If you commit a foul you have to do one or more of these. If you didn't do one of these it isn't a foul. So in this case you are pushing off on a player. So it is a push. It clearly isn't a hold, a block, a hand check, illegal use of hands, and since the player was deemed to do it on purpose it couldn't be a player control foul. So in essence if what the OP said is true it is a "push" foul but probably also an intentional or technical foul type. See chart below to reference foul types.
