The answer is probably "never".
Last week, there were two Jameis sightings. In both, he openly supported the New York Yankees.
On February 8th, Yankees pitcher James Kaprielian tweeted thanks to Jameis for visiting the Yankees training facilities, apparently for the 2017 Yankees Captain Camp.
The next day, on February 9th, Jameis made an appearance at an Orlando Magic game decked out in Yankees gear.
Neither of these should matter. After all, LeBron James was a Yankees fan for years before being seen at Indians games wearing Indians gear. But LeBron leaned on his localness to be accepted as an Indians fan. If Jameis were to don a Rays jersey, it would not have an ounce of authenticity or credibility.
He is a Yankees fan. He is always will be.
The quarterback of Tampa Bay's football team openly roots for a team that plays against and in the same division of Tampa Bay's baseball team. This would be similar to Evan Longoria publicly being a Atlanta Falcons fan or Chris Archer publicly being a Carolina Panthers fan.
The big word here is "publicly". As with the Sternberg-Mets fandom, it is absolutely acceptable if a player, owner, or whomever roots for a team outside of Tampa Bay. But when that fandom is publicly flaunted or discussed, Tampa Bay fans have every right to be upset. Because if the opinion makers believe the local teams aren't good enough to root for, why should the fans?
If I was the Rays, I would write Jameis off. I would not invite him to throw out a first pitch nor be a special guest at any games or outside charity events. I wouldn't even invite him to the FSU Chop at the Trop. If any fans ask (and FSU fans probably have), the Rays should politely inform them that Jameis's fandom is somewhere else besides Tampa Bay. Jameis is not persona non grata, nor he is not barred from Tropicana Field, but if he wants to see a Rays game, he will have to buy a ticket.
That's not to say the Rays shouldn't engage Jameis. They should absolutely make Jameis's Yankees fandom an issue. But they should do it through Raymond.
I have often said Raymond is an under-utilized marketing tool for the Rays. Raymond can go to local events and engage fans at Tropicana Field as any mascot would. But he should also create videos for Rays fans to share on social media.
Raymond should create a series of short online videos - either on Instagram, Facebook, Snapchat, or YouTube - playing up that Jameis doesn't want to hang out with him. These videos would show Raymond wanting to be friends with Jameis, but Jameis not responding.
Raymond could try to play catch with the Bucs mascot only to fail every throw, he could try to call Jameis, tweet Jameis, or cry after after looking at pictures of other Bucs and Rays relationships and then a picture of Jameis in pinstripes. This could be an ongoing saga throughout the season - maybe once a month. Momentum it could build if done right.
Currently, Jameis Winston has shown little interest in the "Team Tampa Bay" concept. He is a Yankees fan and expresses that openly. It is probably not the smartest move, but then again, Tampa's politicians play both sides of the Yankees-Rays local dynamic as well. As long as the Yankees have such a large presence in Tampa, there is no incentive for Jameis to root for the Rays, just like any other Yankees fan in Tampa Bay.
Using Raymond could get Jameis's attention. The skits should be very careful not to annoy Jameis, only to poke fun at his fandom. That's why the videos need to posted sparingly.
As much excitement as Jameis Winston has brought to the Bucs fanbase, it is a shame he can't bring any of that to the Rays.