It's kind of strange that this isn't consistent between all Vita games. How can I determine where a game saves its data (and therefore whether it can be backed up and restored)? Is it game data supposed to show up in "Application Data Management" if it exists? Does it have anything to do with "Memory Required" on the back of a game box? What if I downloaded it, have no box, and the digital manual doesn't explicitly say? Is there any way to tell without purchasing the game?
I believe that all Vita saves are saved to your memory card; hence why you need a memory card to use your Vita and play games. Also, I think that a game only appears under "Application Data Management" if a)It was downloaded from the PS Store or b)If it has add-ons or DLC.
So, in a rather confusing move by Sony, I think that all Vita saves are on the memory card, but if you play them by cartridge, they will not appear under Application Data Management, unless it has add-ons or DLC. Or at least, that's how it appears to be on my Vita.