Besides which, this is not the equivalent of making a bartender clock out during his break. It's the equivalent of making him clock out while he stands at the bar waiting for the next customer.
It might be illegal across the USA, but I do know at least that in Oregon, this is illegal. I know someone that got several hours of backpay for unpaid lunch breaks because someone reported the business for not allowing them to leave during unpaid lunch breaks.
Requiring people to stay on premises during lunch wasn't illegal, but if the requirement was there, they have to be paid during the lunch break. If you are clocking out, then you MUST be allowed to leave.
When I was younger one manager was notorious for clocking us out while we were still cleaning at the end of the night. It went on because reporting it risked having your shifts cut or being quietly let go.
It's the same in the rental market. Where I am, viewing and application fees have been illegal for years but estate agents will still try to charge them. If you bring it up or refuse to pay they'll just find someone else who will.
If you are not paid for that time, they have no right to require anything.
Wtf is this attitude to employees as if they are property.