There is also the PHP setting for time zone.
I was going through PHP to do checks before upgrading from 5.6 to version 7.
I noticed the time zone is set to the country of the hosting provider, rather than the country of the hosted web space customer.
Suggestions
If the plugin displayed the time that it thinks is the actual time, then the user would be able to know immediately that there is a problem with clocks somewhere on their system.
The time would be displayed in dashboard/admin, but also may be optionally displayed in the front end view.
It could also display the amount of time before opening again (fancy option – but useful), or time left before closing.
The plugin could possibly be set to read the times from various systems on the server, and give the user the option to choose which one to use.
There could also be an option to check the time independently on an internet time server elsewhere.
There could be an option to adjust an offset to what ever clock system is used. Have the ability for the user can adjust the offset, so they can match up the displayed time with their actual local time.
Some of these add functionality, and some can be used to help “work around” problem situations where a diagnosis is not yet conclusive.
Thanks