I have since emptied the tank as I was just leak testing it at the moment, but I don't recall any bouncing at all. The hardwood floor underneath it did not appear to be bending under the weight either. My level had the whole thing as straight as well.Do not worry about bridging, it is required for trusses, not joists. I-Joists that you have are to be treated as standard joists and would only require blocking for the diaphragm, which you probably don't need or it would be there already. I-Joists are indeed stronger than standard similar sizes wood joists and they deflect less.
Does the floor feel bouncy when you walk on it now that the tank is full? If not, you're probably fine. If you're still worried, let me know the depth of the joists the tank is sitting on, the size of the flange of the joists (the larger top and bottom peices) and the thickness of the web (the plywood piece connecting the flanges, the piece with the stamp on it you took a picture of).
I made this diagram for another user who offered to help and take a look, but thought it might help here too. I am genuinely very appreciative of all the help. People have gone way above what I could have ever imagined.