Would they not still need watches

I know it is a stupid thread, but I think it is fun to make stupid threads.

In this system in this film, would people not still need watches or other devices to tell what time of day it is. Would you still not have to be at work at a specific time. You would also make appointments with friends and family to meet them at specific times.

Say, when you get off from work, your clock shows so and so much, then you have to remember, that you have to be at work again, when it shows 16 hours less. Then if you buy something, say food, before you get home, then you would have to remember how much you spent in order to be at work again in time.

I did not see any devices that show, what time of day it is.