Thinking about it again: that's so odd a position for JetSmart to take here.
Having adopted AAdvantage as their FF program is an even more complete step than, say, QR took when adopting Avios as the currency for their own Privilege Club program.
In the latter example, QR controls its own reward charts, earning and redemption rules, promotionns, elite status qualifying criteria, status perks, etc.
But here, (as with FJ in future), the partner airlines has gone a step further, adopting the entire AAdvantage program. All the program elements should presumably be identical to AAdvantage, because, AAdvantage is the program. Perhaps they will.be, in time.
Imagine a flyer that qualifies for AAdvantage elite status exclusively flying on JetSmart. If the status perks that reward such loyalty won't eventually apply (when flying JetSmart) it's not clear how their adopting the AAdvantage program is intended to function.