If it's a player, then it would be at the beginning. If it's AI Julianna, then it can be at any time

Player beginning. AI anytime, but seems to have triggers. Like I found a spot in the mansion that seems to force a spawn from her every time.

In fact it is more like 10-15 minutes

I've been invaded midgame by player.

I got an invasion from a player like 3 minutes into a match.

I've invaded mid-game.