What about the filter intake, sometimes they can get their fins caught in them and the suction alone can cause the delicate fins to tear.
Do a test on the plastic plant with nylon hose instead of the toilet paper, run the hose along the plastic plant and if it snags it will also snag the Bettas delicate fins or just remove it all together to be on the safe side
How much salt are you using and for how long? also how much and how often are your water changes.
What kind of substrate are you using, some are sharper than other and that could be the cause or part of the cause.....