The Rays literally can't do anything to generate new fans in Tampa, assuming their marketing division isn't the worst in professional sports. They have no control over their fans, the biggest predictor for getting fans to come to the ballpark is winning, and the Rays are consistently doing that, or building a foundation for future success.
"Cheap owners"? I mean yeah I guess, but if the team isn't generating much revenue, which I can't imagine the Rays are, then a top half payroll just isn't in the cards. Not every team is the Yankees, Dodgers and Boston and can afford to throw a bunch of money at their problems and be profitable in down years, at least the Rays' ownership is keen enough to continue to find intelligent people to run their front office.