The manager, Tom is Canadian, but close enough. The water, ice, etc are perfectly safe. It is a popular spot.
Pretty much the water and ice and food is safe anywhere you go in Cozumel, unless you drink tap water (DON'T).
If you order water, it will be from a purified source and same with ice.
If you drink too many frozen drinks and get sick, if won't be because of the ice they used.