The AS offer is via Cardlytics from what I can tell because it is available for many BofA and Chase cardholders. All this means is that Cardlytics does not get access to your card type, but only spend history. At Chase, it is each card individually history. Usually the filter is something like, if AS previous charges, then don't give the offer for that card (or give the lower 5% offer instead of 10%).

Now BofA does something different as the offer is applied at the account level not card level, so if you qualify you can use it on any card, but all cards are looked at together to determine what offers you get.

Chase has gone further and marked offers as Exclusive when they are not available to other issuers (Kohls). AmEx definitely gets Cardlytics, but they also go after a premium set of merchants with their in-house programs and maybe a special marketing team at these vendors.