Five rules, and only two of them matter.
Wash it however you like — dishwasher included — and keep abrasives away from it. That is the whole of it for a sublimated mug, because the image is sealed inside the glaze rather than stuck on top of it.
Staining happens inside the mug, on the glaze, and has nothing to do with the exterior print. A soak in warm water with a spoon of bicarbonate of soda lifts it without touching the design. Reach for that rather than a scourer — the scourer is the thing that does permanent damage.
Almost every hand-wash-only warning you have read about printed mugs was written for a different product. Check which one you own before you start treating it gently.
