Yes, it needs to be air tight… I often buy barrels with the T piece already attached…
Some people use aroldite, some use silastic, shoe goo, bostic… hot glue, UHU … basically any glue will do … but whatever glue you do use, make sure if the T piece is 2 piece, glue it together first and make sure there are no sharp bits on the inside and it is well stuck… I hate poking the glued barrel into a T piece and the T piece pops in half
Then, clean/sand the end of the barrel to go into the T piece then test fit in the T piece and mark the barrel where it needs to go in to… then take out the barrel again, put the glue on the barrel (not in the T piece) leaving the glue about 5mm from the end of the barrel… then slide and twist the glued barrel into the T piece and make sure the barrel goes all of the way up to the mark you made.
Look inside the T piece with a torch to make sure no glue came forward from the barrel into the T piece… if any, wipe, pick scrape it out… then leave barrel for a decent amount of time to fully set (depending on glue)
Next… order a bunch of barrels with T pieces already on from ebay… (for next time)