I've been poly with my gf for nearly 5 years. I also experimented with poly for 6 months with my ex husband back in 1999-2000.
I won't lie, it's challenging to have them have that first overnight date. With my ex h it wasn't so bad, because we'd know the woman as a friend before he started dating her. (So, the first night wasn't so bad, though I had bad reactions to other aspects of the dynamic.)
With my gf, she's only had 2 bfs since we met. So only 2 first overnights. I was anxious both times. With the first guy, it was because it wasn't a planned overnight! She just didn't come home! I was OK with it til I got to her place at 10 am and she wasn't there. Turns out she missed the last bus home, her phone wasn't working and she was too shy to ask him for use of his phone or computer to let me know.
With the 2nd guy, I wasn't so much anxious about their overnight as I was about the whole relationship in general. This was over when I met the guy.
Now, fast forward to present day. I've got a bf of almost 2 years and just this summer he's started dating someone new. They've had 2 overnights and I am not feeling great about his attitudes towards dating others in general. He is "more poly" than I'd first thought. You can read the recent posts in my blog here for much more on that. Here's a link to the last page of it.