Hi Seth !
Good news about the new Cories!
Although you didn't ask, I am sure some one will let you know that juliis are actually uncommon and hard to get. It is most likely that you have gotten another simular but diffferent species. Perhaps someone else will address that, since I can't remember how to spell the full name of the trilis that are most often taken for juliis.
But as to food: Hands down the best in, in my book, is Hikari Sinking Wafers if they are available, otherwise another bottom feeder wafer or tab--not algae wafers. Hikari Sinking Wafers are for bottom fish, and the Cories always seem to like them best. They will make a good staple for your Corys. In addition, some algae tab occasionally until the tank matures, some frozen food like blood worm or mysis shrimp and perhaps a second or third variety of tropical fish food, such as flake or another brand of botton wafer or tab--for variety. If you can find some live food like river black worms, your Corys will love you to pieces and may get so excited that they do the sexy dance.
But until the tank matures, it will be best to underfeed than to over feed. Uneaten food will turn to ammonia. As a matter of fact it is often recommended not to feed fish for a few days in a new tank, as it all turns to ammonia eventually
Again you didn't ask, but did you cycle the new tank? If not, do several water changes a day, and if possible get the water tested at the local fish store after a couple of days to see how the stats are. Once ammonia and nitrites begin to build they are deadly. If you know anyone with a mature tank, get some filter media from them and seed your filter, or get some Bio Spira to help speed the process. You did not say you had a plan for cycling the tank, you had trouble before, and so I am offering this just in case.