For timekeeping, you're correct that timezones shouldn't affect anything. But in some parts of law, the local time of a particular place (eg state capital, naval observatory, etc...) is what might control when a deadline has passed or not.

If we then have to reconcile that with high speed space travel, then there's a possibility of ending up in a legal pickle even when the timekeeping aspect might be simple. But now we're well into legal fanfiction, which is my favorite sort but we don't have any ~~guardrails~~ ground rules to follow.