Yes, I did press assign. In the line you mentioned, the name of the alien race appeared. However, when I check back 5 days later, they're no longer assigned.
The team is still at full health (5 members), so that's not it.
I assigned another team, to my 2nd player race (Terracorp, which also lives on Earth, like me). This team is still in place.
I also assigned a diplomatic team from Terracorp to the aliens, the difference being, that Terracorp has ships present in the alien system, while Ordo Solaris, my first race does not. Same thing. Team no longer assigned.
Note, that the alien's stance towards Terracorp is also hostile, because I did some gravsurveying in their system. They started out neutral initially. They started out neutral towards Ordo Solaris as well, by the way. I just pissed them off with active sensor bling-blinging in their system. And killing some of their ships in their (I think home-)system, after they attacked me first.
Here comes.
My 3d player race, Vox Imperia, has not visited the alien's system at all yet. They did establish full communications though, in the brief moment that an alien ship jumped into my system, before being blown to bits. The alien's diplomatic stance towards them is as yet 'unknown', probably neutral, since they did not upset them with ships in their system.
I also assigned a diplomatic team from Vox Imperia to the aliens. And behold.. It's still in place.
So I guess, my initial assumption was right, and the aliens kick out my diplomatic teams because we are at war?