You'll end up spawning into the new session where ever the group leader is, I believe. You can start matchmaking from anywhere on the map, so sometimes people won't be at the location. However, once the group fills up, everyone should get the option to hold Z to transport to the mission area. 

When I'm at the entry of a mission area, I have the choice to search for a group. Whenever I do this, I get requests to join other peoples groups. After accepting this request, I'm usually together with the other person at the White House.

I think that's not the way it's supposed to work. In TD1, a group was formed automatically and every new member was ported to the mission area.

Group finder bugged?