PlayStation All-Stars Battle Royale Question

So, I won’t bother you guys with the details, but I have PlayStation All-Stars on my new PS Vita. I have a question about the game’s cross-buy. Specifically with DLC. dose anyone know if the cross buy for DLC will work if you buy on vita first and not on PS3. (I bought some on PS3, and it allowed me to download it to my Vita by hooking it up to the PS3). If I buy it on the PS Vita, will I be able to download it to my ps3, or will do you have to go PS3 first.

I dont think it matters since your purchases and downloads originate from the PS store and your profile.
I bought SkullGirls encore lat night on Vita and it said it is valid for both PS4 and Vita.