Pain Distributor’s second ability triggers whenever a player casts their first spell each turn, not just on their own turn.

Pain Distributor has to be on the battlefield at the moment they cast their first spell. Notably, Pain Distributor’s first ability won’t trigger for you on the turn you cast it, although it may trigger if another player casts their first spell that turn after Pain Distributor is on the battlefield. If a spell causes Pain Distributor to leave the battlefield as an additional cost to cast it, the ability won’t trigger.

Pain Distributor’s ability resolves before the spell that caused it to trigger, but not before you have to pay for the original spell. You won’t be able to use the Treasure token you create to pay for it.