The manager needs to be informed of the dire need for hygienic training among his staff. If she does this, it means she hasn't been told otherwise. That means it is the manager's fault. However, if you give the manager her name, she might get fired. The consequence is too hard. So just tell him you saw an employee sneeze into "their" (keep it neutral, even if it's a grammar mistake) hand and then handle the food. Tell him the hygienic way to do this is to turn and walk away as far as possible from the foot before the sneeze comes. Then sneeze into your elbow.
There are hygiene guidelines for food businesses. Tell him you will come back in the future to check. If conditions aren't better you send a letter to the city's health office.
Till