Adding the First World as a setting doesn't confirm time travel, just like adding Ravnica didn't confirm any changes to your current campaign. Theros didn't mean that Satyrs are in your world and Van Richten's didn't mean that's how the Shadowfell or Domains of Dread work in your game.
Every setting is meant as a setting -- not some giant meta plot. Because if that meta plot existed your characters would have to be 15+ levels, and we know WotC isn't supporting that play.
Quit searching for some overarching connection and enjoy the game at your table.