The mechanics of a connected universe aside, I think what a lot of people miss is that there's a direct connection between Peter and Tony in terms of a shared outlook and motivation.
In CW, when Tony asks Peter why he's doing thus his answer is: -
"When you can do the things that I can, but you don't... and then the bad things happen, they happen because of you."
That is almost exactly what's been driving Tony's character arc since day one. Survivor's guilt. A part of him is still stuck in that cave with Yinsen just as part of Peter is still stuck in that sidewalk with Uncle Ben. This wasn't just them dancing around the by now tired "great power" speech, it was worded very deliberately to resonate with Tony's arc.
One might also consider: of the established characters, who the hell else but Tony *could* be a mentor to Peter? Rhodey? Hank Pym? Vision? I don't think so somehow.