Depends on what the employer wants its cashiers to do. I worked briefly as a cashier in a just-give-them-their-change-and-keep-it-movin' place and some lady counted back her own change for me hoping to teach me a lesson. I smiled politely and kept doing it the way bossman wanted.
On the off chance that your bossman is listening:
Dear Bossman;
Please instruct your employees to hand change to the customers in two separate lots: coins first, then bills. This allows the customer to take control of the coins without the bills getting in the way. It reduces the probability of dropped change and keeps the line moving.
Thank you.
-A. Bustard