For me it varies by situation. Since my husband and I became poly (again) for people HE is dating, I met one of them (and her husband) after their first meeting, when the four of us met for board games. I met one woman for lunch (the three of us) a week after their first date. I met one of them for drinks solo about a month after he started dating her. One woman who is long distance doesn't have much time out here, I will meet if they ever move their relationship to err...past second base?
I will meet anybody he is dating for SURE when they decide he would like it to be a sexual relationship instead of a cuddly friendship, but he likes me to meet people he likes sooner than later anyway, as he usually thinks we'd really get along. he moves slow so I have met anybody he likes a lot sooner than it moves past anything other than kissing. We also both prefer that he meets anybody that I plan on dating if I decide it's going anywhere other than friendship. However he just met my boyfriend for a few minutes once, after a month or so of dating but before we became sexual, and that was enough for him. So whatever works for your comfort level is good, in the past I've met other partner's partners at our local sex positive club events, cuddle parties, and at regular old fashioned dinners. I always like coffee at some quiet large coffeeshop, just like my first dates, things can be kept short if it's uncomfortable, you have something to hold if you're nervous
and if you end up hitting it off as friends, you can go back for seconds and hang out longer.
I didn't meet my boyfriends wife until after things were sexual, a couple of months in for coffee, just the two of us. I find it unlikely I will ever become sexual with anybody again unless I have met and talked with their primary(ies) first.