This is what I was always taught...
Catholic Encyclopedia, 1911
Seems simple enough to me.
Yes, this seems to back that the UA is to be understood with regard to the election itself.
So in those historical cases where the Church came to accept another, the Church was in fact materially mistaken regarding the true identity of the pope.
Some theologians took UA so far as to say that even a false Pope would be convalidated by UA. We now see that as demonstrably false from cases like that of Anacletus.