Your concerns are completely valid, tub-to-shower conversions do generate a lot of dust and debris if not handled carefully. A good contractor should absolutely be sealing off HVAC vents, laying down heavy-duty floor protection, and using controlled demolition methods (scoring tile rather than just hammering it) to minimize spread throughout the house. For the concrete mortar bed specifically, ask about wet-cutting techniques, which dramatically reduce airborne dust.
While my experience is more on the kitchen side, I recently worked with some Oakville kitchen designers who were incredibly methodical about site prep and dust containment during a renovation, the same principles apply to any skilled trades team. A company that takes that kind of care in one room will likely bring the same discipline to a bathroom conversion.
I'd suggest asking any contractor you interview specifically how they handle HVAC protection and what floor coverings they use. If they can't give you a detailed answer, that's a red flag. Companies that specialize in renovation rather than just general contracting tend to be much more surgical about this kind of work.