Humanity didn't need to develop time zones until the widespread use of railroads forced the issue. Until then, each city and town had its own time and its relation to the time at the Prime Meridian was only important for determining longitude. Europe was a patchwork of different calendar systems after the Gregorian calendar was established because it was too Catholic, let alone other civilizations keeping their own calendar systems as Europe hadn't taken over the world yet.

My guess is that it will all be dependent on the second. My guess is that the second becomes standard to humanity as it is baked into so much technology that it can't be replaced with something else. Every other planet will have the second and design their own timekeeping around that. If a standard is needed across planets, they would probably either use Earth UTC or a way of displaying Unix Time directly in a form which people can directly read.