You should not worry like some inteligent posts already asnwered your concern just be sure to be ur fish translator when its interests them, that is if u r home and its not mandatory for u to be home either.
Anyhow, I had to call them for our a/c later that week and went into the office and they were like "you're the one with all the fish tanks right?" and then when I told them I was they pretty much said they don't have anything in the lease against fish tanks so it's not a problem but if one of them breaks to definitely expect a bill for over 1,000$ from them that I'll be responsible for which I told them was fine because it is my tank and would be my responsibility if such a thing did happen.
The bill would be much, much higher than $1000. Probably 10 times that. Not only would you be responsible for damage to your apartment(carpet, drywall, etc would all need to be replaced) but you would also be responsible for replacing the belongings of the tenant below you and responsible for the repairs to that unit as well. If you have large tanks you should always be carrying renters insurance with liability coverage.
The owner of the property has insurance to cover any tennannts.. Say I leave a cigarette burning and the apartment burns dowm I would not have to pay for damage to his building the insurance would cover it. D on't worry you pay his premiums with your monthly rent check.