about the "secondary processing" (二次加工) when i was reading the manga, "derivative work" (二次創作; lit:secondary creation) came to my mind immediately. Derivative work includes anything from doujin, cosplay, fan games, fanart and so on... In both case we have a primary work remixed into a secondary...
First of all, i confirm that アフター does stand for "after party" (though Muyu misuses the slang).
Regarding "Ao Tita" it's obviously a short for the longer name we can see on the gacha machine.
It reminds me of "Blue Archive" for some reason which is shortened into ブルアカ (Blue Aka) in japanese.
if...