Does getting inverted matter? Maybe. It all depends on how fast your jump is and whether you can get to the invert and start the turn soon enough in your jump. Forcing an athlete to invert can actually slow down their jump and create jumps without turns.
When watching a jump and looking at the off the ground sections there are three distinct sections, take off, swing, and turn. Every jump needs those sections. There are times that you have beginners, especially an athlete who is weak (cannot do a pull up), that cannot even get to the turn before the pole gets to vertical. Those athletes jump without a turn.
As far as an invert this happens when the athlete is fast enough and strong enough to finish the swing and get their hips above their hands before the pole gets to vertical. At that point they still have time to turn and push off the pole before the pole goes past vertical and they can successfully clear the bar.
The jump speed and pole speed need to match up. No single position is more important than the “flow” or movement of the jump. That is why a beginner, who cannot do a pull up, probably won’t even turn because the pole reaches vertical before they can turn.
So when coaching an athlete, or coaching yourself, make sure to not force an invert unless you can get to that position early enough in the jump to capitalize on it.