You don't get a special mobile shopping discount. You get a discount for your linked affiliations which would be the same if you checked out at a register and showed you Magic Mobile pass, AP/MK, etc. The app doesn't increase your discount tier in any way.
If
@juliebee got a 20% discount at World of Disney with a
DVC discount using mobile checkout it was at WDW's World of Disney in Disney Springs, not DL's World of Disney in DTD. The only 20% merchandise discount that would automatically apply at DL is the Inspire Key discount which is 20%.