There is a lot of speculation when it comes to Varys' motives. That's a particular part that never really made sense to me, because in the books he seems even more inclined to help the Targs. The show at least has seemed to paint him as something of a "prepare for everything" kind of guy, so he says the right thing for the right situation (in this case, agree with Robert that she needed to be poisoned). That being said, what if Jorah hadn't intervened?
I don't know how much they intend to veer from the books with that plot thread, but if they stick to them, it will get even MORE convoluted later, although it does at least seem like he has always been for bringing the Targs back in some capacity, if only to wipe the slate clean. It seems like he'd also be okay with someone like Tyrion ruling, as, as he has stated, he's more for the good of the realm than some shmuck having a power fantasy.