To me there's two different sets of people saying "join our relationship" etc, the first is the poly-newbies who are honestly hoping that their unicorn-hunting fantasy will come true and a HBB will join them and love them both equally and everything will be amazing, poly-fi, secondary etc etc.
The second set, which applies to me personally, is the group of people who simply prefer triads to other relationship configurations. For me, saying I'm looking for someone to join our relationship shouldn't hold any implications of unicorn-hunting, because that's not how I view relationships, but I will admit it is probably a lazy use of language on my part. The thing for me is that saying "I'm looking for someone to join us" is far simpler than saying "I hope to find another person that we're both interested in, to some degree, who is also into us, to some degree, that we could form a whole cluster of mutually enjoyable and beneficial romantic and sexual relationships, together with no prejudice based on previous relationship status and with no unrealistic expectations other than to be totally honest with each other and let things develop naturally."
If I had to type that out every time, I'd get arthritis in my wrists in no time
Saying "to join us" is just a short-hand way of saying that for me. If you think about, any relationship is a joining of two people, it's just that saying you're looking for someone to join me/us is simply from my perspective. It doesn't mean that I think the other person doesn't have a perspective, it's just a way of phrasing it.
To me, it seems like a lot of people say something without carefully considering their words, and so people assume things that weren't necessarily intended, and could've been avoided with a better use of language.