I hate dust sheets with a passion! Had more trips and slips with them than anything else, give me a nice safe power saw or ladder anytime!
That dust sheet on a tiled floor is an accident waiting to happen.
You can get rubberised dust sheets which will grip smooth floors, but they are no good for pile carpet as they "walk"I use the disposable plastic sheet on cabinets etc it can be heald in place with masking tape and lifted up and laid on top of the cabinets overnight cardboard taped to worktops works well. Standard dust sheets on carpet can be taped in position.
As for clearing up fold with the rubbish inside then tip it out onto a easily cleaned surface vinyl or outside on concrete then vacuum it up and shake the dust sheet outside, my dust sheets were washed at least once a week.
With a tradesman he cannot dust sheet cards, vases, and plants they should be cleared away before he arrives.