Yes. They can get extremely mushy if not properly cared for. Heck, they will turn to mush even freshly fileted if not cared for. Spotted seatrout are in the drum family and have extremely clean, flaky, and soft/tender meat. They are not bloody, and don't need to be bled like many other fish.
But it's really important to cool them down rapidly after the catch, especially like now as water temps are in the upper 80s. I put mine in a saltwater slurry in the cooler as I keep fishing. Throwing them in a livewell is a recipie for disaster as they will die quickly and begin rotting in hit summer water temps.
Also, they need to get completely firm in the slurry before cleaning. This keeps filets firm so they hold together. (Supposedly its fine to even wait till the next day to clean them if they are in a slurry... but i havent tried that). I also have an ice bath I leave the filets in as as I'm working through the cleaning process.
If you do this, then freeze them in ziplocks with water or vacuum seal, they do great frozen for a later date. If you let them get at all mushy before you freeze, they will completely fall apart after thawing.