I think VOY handled it in the correct way. They could not have possibly known about new uniforms.
Yet somehow they learned about the new, slimmer hand phasers, long before they made contact with Starfleet...
The exception being the Wrath of Khan uniforms, which they kept for 70-something years.
Pretty much exactly so - 2278 was the earliest confirmed appearance (on the Bozeman
crew in "Cause and Effect"), 2348 the last (on Jack Crusher in a holomessage recorded at Wesley's birth in "Family"). Although the uniform did change a bit along the route, and we might say this jacket-plus-pullover style was in use in TOS or Pike's days already - it's just that our heroes only wore the pullovers without the jackets when Starfleet wasn't watching.