Every screen evaluates its schedule against its own local time.
Schedule a playlist for 09:00 and it starts at 09:00 in each city it is assigned to, not simultaneously everywhere. For most signage that is exactly right, and it means you do not think about time zones at all.
Where a screen gets its time zone
From its setup. A screen keeps that time zone until you change it, and you can change it if the screen moves.
When you want the opposite
Occasionally the point is that everything happens at once: an all-hands, a countdown, a company-wide announcement timed to the minute.
For that, set every screen involved to the same time zone. They then share one clock, and a schedule fires everywhere together regardless of where the screens are.
Doing it per screen rather than globally means you can have both: a synchronised set for the announcement, and everything else still running on local time.
Clocks have to be right
A screen keeps its clock over the network, and a screen whose clock is wrong runs your schedule at the wrong time. See Configure time servers if a screen cannot reach one.