@thunkybunny, whoa... A little slack, please. If jphillmore has just seen this woman a few times, and she told him up front that she's poly without it bugging him, it just might not have occurred to her that he'd feel torn up over this. It doesn't sound to me like he has the grounds (or the desire) to cut and run just yet... Let's all talk more and sort this through?
@jphillmore, I hear you. The first time you see someone you care about with someone else is a strange moment, even if you knew it was coming and you're happy for them.
I definitely recommend riding the strongest wave of feeling out, and seeing how you're doing once it passes. (I also don't suggest drinking when you're down about it, but that's totally your call.)
Something people say on here, and in other poly resources, a great deal is that the first rule of poly is communication. You have the responsibility
to tell the woman you're seeing that you felt this way, and the right
to have a conversation with her about it. There's lots of communication recommendations elsewhere on here; I suspect it's a common tag for posts.
If I were your lady-friend, I'd probably apologize for freaking you out, and apologize again for not noticing how upset you were. I'd also offer to lessen the volume and intensity of PDAs I exposed you to, and then to either let you get to know my other lovers in some other context (bowling, bar-hopping, movie night, whatever) or to have space from them while you sorted your feelings out... Of course, I don't actually know her or the relationship structures she's a part of, so I have no idea what she'll actually do.
Good luck, and keep us updated!