Using "push over" when the action is actually pulling would not be correct.
You can, however, say "pull over" to mean that you pulled something/someone and it fell over as a result. The definition you quoted is one meaning of "to pull over", but it is not the only meaning. For example, this makes perfect sense:
I pulled the chair over and it landed on the ground.
In general, if you use "pull over" with a vehicle of some sort, people will assume you mean the sense of stopping it by the side of a road. If you use "pull over" with something that is not a vehicle or something you ride/drive/etc, then people will generally assume you mean you pulled it and it fell over, but it will sometimes also depend on context.
You can, of course, add extra text if you want to be sure people will know which one you mean:
We pulled the car over onto its side.
(This clearly means you pulled it and it ended up lying on its side, not that you made it go to the side of the road and stop.)