Hello Luca,
I mentioned this in a different forum (I do not have permission to mention on RC)
For feeding any food specifically for them...I would be lieing if I told you I did. I can do a run down of everything that is currently being added to the tank if that would help you out. They are kept in very high flow (close to a Vortech MP40 & MP10) and kept in close to the darkest section of the tank. Not like there is a whole lot of light being used over the tank to start with (2 PAR38 LED spot lamps lamps are used 4 hours each for the day).
Water changes are done Wednesday & Saturday, 16 gallons, ESV salt, Magnesium adjusted up to 1400, and salinity at 35 ppt.
For liquids that are dosed other than the Reef Nutrition foods (Shellfish Diet, Rotifeast,Articpods, Oysterfeast) are 4ml Fauna Marin MinD is added a day as well as 4ml of Methanol.
This does not include the dry feeds that are also fed into my tank (Fauna Marin MinF, Clam, SeaFan, Zoa/Acan foods).
Now for your situation since it is not going into a tank set up for specifically filter feeders I will give you a few options (besides the wise guy remark of sending it over to me). First, for your tank I would personally keep it out of direct light, dont want algae to possibly grow over it. Second, it is going to need a decent amount of flow going over the tunicate colony. Third, at minimum have a phytoplankton source (for example Phytofeast by Reef Nutrition) and bacterioplankton source (easiest for your situation would be to set up a bag of bioballs prior to the return pump and shake the bag a few times a day. This will allow the films on the bioballs to enter the tank for a food source for the tunicate).
Mike