Uuuh this sounds confusing, so let me try to clarify that.
The first (first as in A first, B second, C third etc) MAIN Eidolon of any element is what your friends see. That means that if you have Diabolos in team C and a proper Dark Eidolon - let's say Anubis - in team F, then nobody can see Anubis. Because Diabolos already took the Dark part of your Eidolons.
So, make sure you have proper, usable Eidolons for all elements available for your Friends to use.