Sometimes it's actually built into the game, so there isn't a online pass / download. This was the case with Battlefield 3 and a few other games. Not sure why yours is different, but perhaps take a look at the listing and see if the online pass is free. You might need to "purchase" it. I know the cross buy Vita games give you an "entitlement", which changes the store price of the game to free.
I added it to my cart and got all the way to checkout, and it show $9.99 the whole time. Even reduces my wallet balance at the final screen before confirmation. Not sure what's going on with it. Maybe I'll give the Sony folks a call.
Edit: checked my services list and it shows the online pass for both Vita and PS3 versions. Wen I try to go into the online features it tells me I can buy a pass or redeem a code. I just tried to do the buy a pass option (tried redeem and cancel earlier) and it tells me I have it installed and lets me into the online. Before I was trying the buy option from the store. Weird, but glad it works.