Could tell them honest and up front.
"I'm poly, partnered, and also enjoy casual sex. I'm not looking for serious at this time. I'd be up for a hook up/on night thing. Are you up for that?"
If yes? You negotiate safer sex practices and location. If no, you say a polite thank you and move on.
Has anyone had a short term partner (hookup not expected to be more than once) react negatively towards the existence of another partner?
From
your other thread, you are in a monogamous relationship.
I hope you are just thinking to future and how you would deal with being single poly or partnered poly seeking hookups.
And not thinking about having hookups on the side and cheating on your monogamous agreements. And worrying about the hook up partner telling your established partner and you being found out.
Some people don't care if the hook up partner is actually cheating on someone. They figure it's a one time hook up, they aren't responsible for the health of that other relationship, they aren't the one cheating on agreements because it isn't their agreements, etc.
Other people do care. They want a "clean" hook up. And don't want to be deceived into being some sort of "cheating affair accomplice."
The people potentially hooking up have to sort out all their negotiations themselves according to what they care about and value.
In a polyamorous relationship, is it always necessary to tell a hookup or one night stand about your relationship(s) before engaging in anything? When is the right time to bring it up with potential dates or partners?
In the end? When developing your own personal standards that reflect what you care about and value? YOU have to decide when you tell, how you tell, when it "counts" etc. That's why it is YOUR personal standards. They don't have to be like other people's.
Galagirl