Two weeks have gone by. The President now says she has found another vote in a ballot box, and that the vote was a tie. She says that the fill in will become the two year member and the elected member only one year.
Was the vote a tie? - Anon., Sep. 30, 1999
A:
No.
The election was completed when the result was announced (or, if the winner wasn't present at the time of the election and hadn't consented to his candidacy, when he later accepted the position).
(See RONR pp. 436-37.)
The ballot found in the box is irrelevant.
Unless your bylaws state otherwise, if the result had been a tie at the time of election, a re-balloting would have been required, not - in effect - a second vote by the president breaking the tie.