You got the chain of events in 1492 incorrectly - Alexander Jagiellon took the throne of Lithuania a month before Jan Olbracht did, and Jan Olbracht became the King of Poland because of Alexander's own decision to withdraw from the competition.

The date you mention, June 1492, was when Jan Olbracht and Alexander's father, Casimir IV Jagiellon, died - but that does not mean that it's when Jan Olbracht became the King of Poland. Unlike Lithuania, Poland was not a hereditary monarchy and the passing monarch could only give advice on which heir the Polish Sejm should choose in the next free election - and Casimir IV advised the Poles to elect Jan Olbracht. This free election took place two months later, on August of 1492.

Lithuania did not have a tradition of royal election, and was a hereditary system where the monarch was able to name a heir as his successor on his whim. Casimir IV named Alexander Jagiellon as his successor, and on July of 1492, the Lithuanian Sejm gathered to confirm Alexander as the Grand Duke of Lithuania. It was not an election, but a confirmation of the will of the previous monarch.

On August of 1492, when the Polish Sejm gathered to elect the next King, Alexander was a prominent candidate among the nobility - but Alexander himself chose to not compete and advised the nobility to elect Jan Olbracht instead. He ended up elected in that same Sejm.