I've hired employees and promoted a manager... but when I leave the premises to go home, everyone leaves. I clicked on the manager to "mind the store" but still everyone leaves. I downloaded the fix for checking in on the business, so hopefully it works. But does anyone know how to fix this problem?

It's supposed to do that. That's not what "mind the store" does.
When you get home you can call in to check with the business, and you'll get some income from it, even if you don't go to the lot to run it that day, but it won't continue to run when you leave; that's just not coded into the game.

So it still runs itself when I'm not there? and I still make money from that?

What does "mind the store" mean?

"Mind the store" just makes the manager run around cleaning, gardening and hasseling the other employees, yelling at them to get back to work.

You won't earn as much on days you just "check in" with a business as you do on days when you actually run it, but if you have made a decent profit for a while, you will get proceeds when checking in with the manager, so in a way, it does run itself when you're not there.