I do not believe or remember it specifically stated that Shalltear had anti-time equipment, but considering how Ainz clearly stated he knew Shalltear's entire build (Episode 13 for anime, in light novel too iirc) and fought specifically around her and had previously stated that time countermeasures were important in the fight against Gazef, it makes sense that Ainz had a reason for not doing so.
Now, against Gazef, even the episode itself is named Player vs Player, since Ainz respected him enough to take him seriously like a player would, even stating that time countermeasures are important in PvP combat. This proves that if he believes his opponent does not have time resistance, he'll likely use it.
This is mostly speculation, but so is a lot of this fight. The Mind Flayer would likely use a mind attack first, which would fail due to mental immunity. Ainz would likely use any of his hax spells first, including Grasp Heart and Time Stop. Now, some info for Mind Flayer's resistances to these measures would be important, but given that the staff of Ainz Ooal Gown boosts Ainz's racial abilities, which can be found on the Overlord wiki or by watching the show, which would likely contribute to his mind resistance and various other abilities, as well as boosting his Aura of Despair (It's stated the staff of Ainz Ooal Gown can boost Aura of Despair until it effects level 100 NPCs, and that's just an example).
Over all, while it has the chance to go either way, I believe Ainz wins because he has better resistances and more versatility and items for such.
Edit: Overlord wiki defines his mind immunity as a basic undead trait, so the Staff would boost it in this fight. As there are no restrictions, I'd say he has it.
