By the graphic, a player doesn't have to quarantine if exposed after vaccination, so either he caught it (vaccinated or not), or he was not vaccinated and exposed. Either way, we're screwed right?
Correct.
Based on all currently known/suspected information I would say it is very likely be tested positive despite having been vaccinated. He will need to test negative before he is cleared to play. Even asymptomatic COVID cases linger for at least a few days. I am guessing he is quarantined for 5-8 days.