As far as triggering the events goes, it's not actually RNG. I tested it a good amount and found that if you want to trigger a certain event, you generally have to visit the same room twice (for the bathroom, kitchen, hallway and at least some of the living room events), and you have to be sure to visit them while Alice is shown to be there. The only exception I can find is the bedroom event where Alice has fallen forward and gotten pinned, which you get by visiting the bathroom and then the bedroom in the last two day segments.
Also, at least one event is only unlocked after other ones. You have to finish a fair few of the bathroom scenes, up until (I think) the second actual sex scene where Alice lets you cum but makes you finish outside (in the first she doesn't even let you finish). After that, you *have* to do the pinned bedroom sex scene mentioned before in order to get the last bathroom scene currently available (in version 0.3.9, anyway)--the one where Alice finally lets you cum inside.
Also also, to maybe nobody's surprise, All events have a points threshold of which I'm not aware. Some are mentioned in the dev's patch notes, but most, as best I can tell, are not. If some hero could figure out what the events need point-wise, that'd be amazing.