I highly doubt it's made out of petricite. Jhin is a mage after all and relies on his magic to infuse his bullets. Direct contact with petricite would not only drain at his magic, it would also hurt him continuously (or at least be very uncomfortable). Additionally, as far as we know he has absolutely no connection to Demacia.
Since he used to work for a travelling theater and given his personality, I think it's most likely that his mask is fashioned after those usually used for stage performances. My guess would be a light wood that is either naturally white or painted.
Where'd his gun come from?
It was supplied to him by his patrons and was part of the Kashuri armory, I think. Although it uses hextech technology, it was crafted by an Ionian smith. (I'm sure 4 Step Cadence will correct me if I'm wrong on this one.)
And the newly established timeline also doesn't line up! Jhin was reigning terror on Ionia before Sylas broke out and the mageseekers were called upon or even particularly necessary, was he not?
Mageseekers were present before Sylas' revolution. In fact, they are the very reason he was imprisoned in the first place and a major contributor to the suppression of mages that made them revolt.