The sophomore slump is this mythical beast: the perpetual fear that a successful rookie will collapse for completely unidentifiable reasons. Sometimes, that does happen -- as happens with players at any stage of their career, every season. But there's little evidence that the sophomore slump is a thing, and lots of evidence that players consistently get slightly better between their first and second seasons.
This is also true of quarterbacks, unsurprisingly. Of 18 first-round rookie quarterbacks to have started at least eight games since 2006, 14 improved in their second year, according to SB Nation's Adam Stites. Quarterbacks improved across the board, though the biggest differences were in touchdowns and interceptions.
In other words: Jameis Winston is highly likely to improve in his second season, with fewer interceptions and more touchdowns the most likely result. Incidentally, those are two points of emphasis for the Bucs this offseason: reducing turnover, and increasing red zone efficiency have both been consistent talking points for Dirk Koetter since he became the team's head coach.
Winston wasn't even bad in terms of touchdown-to-interception-ratio last year: he had 22 passing touchdowns and another six on the ground, versus 15 interceptions and six fumbles. That interception total is on the high side, especially given his relatively low number of 535 attempts, but it's very much within acceptable limits. If he can cut out a few of those turnovers while adding some red zone touchdowns, the Bucs offense should do just fine.