Hi there, so people didn't have a concept of "timezones" because timezones are an arbitrary invention. But people did understand that local time varied in different parts of the world, dating back to classical antiquity. Here is a similar question I answered awhile back:
https://www.reddit.com/r/AskHistorians/comments/3uufv2/_/cxhy3fd
Specific to ships and timing, you may be interested in this comment further down:
Hope this helps!
They could tell that time of day varied by location since long ago. They had basic timekeeping, and there are certain events (like eclipses, say) that happen on a scale that could be observed from different regions.
I do recall that there was a bit of excitement when Magellan's expedition returned from circumnavigating the globe because their logbooks showed that they had lost a day. They knew that would happen, but it was the first time they had direct confirmation.