I don't know of any that are different, but salary law is consistent enough to know that the salary starts when the employee begins work, so in this case, moving the start date up is what is happening even if the employer isn't acknowledging it. The same goes if the employer says the start date is 1/1 but you only show up at 1/2. The salary starts when the work starts, and doesn't stop so long as you show up once a week or so.
From California but similar everywhere:
> Pursuant to California law, an exempt employee must receive his or her full salary for any week in which the employee performs any work without regard to the number of days, or hours worked.
If employers don't like this, they can pay overtime instead.