I had only 1 tribble, gave it to my Science Office yesterday, when I logged in today I found 3 more in my inventory. Either I didn't notice them or they breed, hope I don't find 6 tomorrow.
As long as you have food they reproduce. But it's actually a good thing as there are certain "breeds" that give extra buffs. So the more you grow the more likely you are to get a supertribble.
I don't remember what thread that was in, but the person who started it even gave screen shots of the breed info. I just got my first tribble today, and put it straight in my bank with all the food I have. Hopefully they continue to breed when you're not online.