I suspect that you're running with excess roller pressure. The pressure is massaging the tire, and slowly walking it around the rim causing slack areas to form.

This may be compounded by an oil film on the rim, or something else making it slippery.

1- keep tires full to near max pressure
2- adjust roller pressure to the least amount that prevents slippage in normal use at full rpm. This may still allow slippage with sudden acceleration, but that's not a problem since it's not how you actually use the trainer. If the pressure i8s right, the tire will only be slightly depressed at the roller contact point, and you can make it slip if you yank the wheel while holding the flywheel. (but not easily).
3- if all is OK and you've minimized roller pressure, and still have the problem, remove the tire, clean the inside of the rim with acetone, mineral spirits, or 90% isopropyl alcohol. Do the same for the tire's bead area, but using only dish detergent and water, and rinse well.

If you've done all the above, and still have an issue, it might be the tire, but I'd be surprised.