Moridin comments on it:

Too many of our number threw themselves into contests with al’Thor when he was presumed to be weak. M’Hael instead earned Lews Therin’s trust, then took charge of the training of his weapons.

The way this is worded leads me to believe Taim either took initiative on his own, or that Moridin was behind this move. Given his promotion to Chosen I tend to think Taim seized the opportunity in front of him. He could have met Demandred at anytime ... Seems most likely to have happened post-Cleansing since Demandred seems to have very little knowledge of the Asha'man at that point.