I agree it could have been handled better but it's not so simple. Jill is under a time restraint because of Tybalt's coercion, so it was a bit of a now or never type of moment for her to be able to get closer to the MC before she had to stay away. And if you don't go with Jill in that moment she doesn't get to hear the story about MC's mom and that's an essential part of what solidifies her feelings for the MC. You change the time and context of the situation when she hears that story and it won't have as much of the same impact as it does during the date.
I think the way Jill's character is written would hint towards her not making such a rash decision.
You've already had a successful date, and if you played it right, groped her and kissed her twice. Bella likes you by that point, which is a huge plus for Jill.
Plus as soon as you tell her you had to cancel to care for a sick friend, she is likely to be all the more interested in you.
The on/off switch with the relationship definitely seems a problem of story telling or pacing, which is pretty unusual for the game.