I wouldn't waste any more time on that alternator. It's a POS. You can tell 'em it's setting off your battery warning system and try an get a refund, or try another alternator, but it'll likely be the same. They do show a Motorcraft 110 amp alternator in their inventory, you'd have to ask for it. It's about $60 more than their crap store brand. Maybe you'd have better luck. Tell 'em their store brand is triggering a charge problem and you want to exchange it for the Motorcraft
F40003332750MTR unit. They should do that without too much hassle.
Alternators at Rock Auto