If the price only changes when the store is closed anyway then there is no issue.
Which is not, in any way, related to digital tags. Believe it or not, employees could change the paper tag during business hours, too! And management could even change the price in the computer system at the same time!!!! It's amazing what technology and a little elbow grease can do!!!!!!!!!!
Which is to say, unless one is droolingly stupid or clinically insane, prices will not change during business hours.
With paper labels, we have a specific process every week for price changes:
If the price is going down, we change it in the computers immediately, then put up the labels as there is time. If the price is going up, we prioritize updating the labels with a specific deadline it must be done by, and then change it in the computers. Either way, if there's a difference at the register, you're being charged less than the label.
If we had digital tags, it would all be 100% automatic outside of business hours, and you'd never see a difference at all.