Burrow, Higgins, & Chase's Deals

[samhain]

Honest question about contract extensions.  

If a player is extended, does the extension generally begin the year it's signed?

Example:  Burrow signs for 50 mil per tomorrow.  Is 50 mil his annual salary in 2023 or does he remain on his rookie rate until the extension kicks in?  

I always assumed the team tore up the current deal and immediately started paying at the rate agreed up in the extension.  

Am I wrong?