Sensei's Divining Top vs. decking

Marek reported:
See the attached log
On the last turn, opponent's library is empty (after being hit with the ultimate of Jace, Mind Sculptor). In reaction to my game-winning activation of Ajani Vengeant, AI activates Sensei's Divining Top to draw a card... and stays alive despite having an empty library.
Until Ajani resolves and kills it, that is, but still...
See the attached log

Until Ajani resolves and kills it, that is, but still...