Chase terms are never clear enough to know the answer to this. The terms say "Offer valid one time only" which I define that your can only get the $100 credit once. So now the question would be if multiple transactions adding up to $500 will trigger this one time $100 credit? Or like you asked, does it have to be a $500 or more transaction for you to get the $100?

Regarding UR, if you redeem UR for the entire transaction I doubt it would trigger the cashback, but I was thinking that if I needed to make a larger purchase (for example $1k+) and covered part of it with UR, and $500 I would charge to the card with the offer, then I believe I would get the cashback.