There are really a lot of factors preventing the Bobcats fan base from growing currently, as others have stated. I don't know if its all entirely reasonable to expect all of the transplants to automatically change allegiances either. I lived in Indiana 15.5 years, then moved to Florida for 8, and have been here for 2. I am a Bobcats season ticket holder (I love the sport of basketball, and specifically the NBA). But my memories of watching the Hoosiers and Pacers with my father, of growing up in the Reggie Miller era, etc will never go away, and they contribute to me being a lifelong Pacers fan. I have watched them on League Pass for ten years even after leaving the state. However, I cheer for the Bobcats when they aren't playing Indy and want the team to do well. I own a handful of Bobcats shirts I wear around town on a frequent basis too.
Now, transplant Pacers fans are probably never going to become a problem, but you have to consider these big name teams come in with large fan bases already (with not all of them being from the original area). So its going to happen. I think realistically you need to hope that the natives will make memories here, and the transplants will support the home team. This will take time, but once the team starts winning some more games, it will come. Even this year alone there is more of a buzz about the Bobcats around town (it helps that the Panthers are abysmal).