I can’t comment on these planes in the sim, but in reality it is a huge no-no to be pushing the nose down after main gear contact. You should never have to do that.
The reality is that the nose gear will come down like a tonne of bricks anyway, and therefore it has to be flown on to the runway, particularly in jets. It goes without saying that the structure of the nose gear is much weaker than the main gear, so it needs taking care of.
It is something you tend to see with new pilots (and we’ve all done it!) where when they start out once the main gear touches down they relax and think job done, forgetting about the nose gear. Before you know it your teeth are somewhere around eye level 
Assuming the flight model is correct (and given the jets you’ve listed are more game-like rather than sim-like I wouldn’t be so sure about that), if you’re finding the nose rising after weight on the main wheel there could be a number of causes;
- You haven’t armed the speedbrake / ground spoilers or they haven’t deployed
- You have too much aft trim
- You have touched down in too high a nose attitude
- You are too fast
- You have over flared
- You still have thrust on
…or a combination of some or all of the above. I can’t say I’ve noticed this behaviour in the 2 jets I fly in the sim, the PMDG 737 & the Fenix A320. I also never saw it in the FBW A320 either.