There is a separate paragraph for that in the Process Agreement.
It appears to be written that way to bring the AAI pilots up to SWA pay rates and work rules during integration so that there aren't people at AAI on a B scale still operating on the AAI side while other pilots go to Dallas and start making SWA wages for the year or more it takes to get everyone trained and under one ops cert.
Otherwise people would be screaming bloody murder, especially the 737 overwater crews that will be the last to go over per BJ. All those interim benefit and compensation changes to our CBA are ALPA's to negotiate. Permanent rates are SWAPA's. It's pretty clear in the Process Agreement.
There's nothing stopping them from doing certain parts early (we hear pass bennies on SWA are next month), but I personally doubt the compensation will happen sooner than SOC, much less sooner than SLI, but what do I know,,,