The user can choose their time zone when they sign up, and the service can prevent them from changing it (or heavily limit how often it can be changed)
The sibling comments are a perfect demonstration why projects tend to balloon in complexity and ever-increasing requirements just to deal with rare corner cases.
YAGNI. A niche tool whose selling feature is time-restricted usage shouldn't have to account for weirdos that miss the point of it and cheat with their clock.