Clearly, there are differences at each store and each MA will have their own way of working. Also all stores are laid out differently and some are so small there is barely any room for extra hygiene materials. ETA: Might be worth asking if you cant see any qtips etc around.
At my store (UK) we have cotton pads, tissue (alcohol and various throw-away applicators) and wipes by the lipsticks and blushers.
Qtips et al around the eye MU and at our makeover station we have everything including eye MU remover / skin care.
We have tissues and wipes dotted all over the place.
I suggest you all get to know your local counter and what your MAs prefer and if there are hygiene materials around, its because theyre there to be used. If you want to try on your face, thats what we the MAs, are there for - armed and happy to help!