I'm surprised that would be interpreted to include time zones. Units of time, arguably (measures), but time zones? Time zones are not a measure of anything. Time zones do not follow on from definitions of units of time, any more than road speed limits follow on from the definition of a mile.

I would be less surprised if it were the commerce power used to uphold time zone coordination - for the promotion and regularity of interstate commerce etc etc. Tenuous, but consistent with a lot of the other nonsense that's been hung from the commerce power over the years.

Then there's the actual enforcement angle - time zones are just a social convention whereby people in a given area pretend that the time is slightly different than it 'really' is (local solar time). There's no reason local / state government and businesses can't post / operate on different hours, and leave federal bodies to operate on whatever 'federal time' they want. This already happens in parts of the world where the official time is locally inappropriate, such as Eucla in Australia or Xinjiang in China.

Obviously the optimal solution here is to coordinate a time change at all levels of government, but failing that there are other options.