FWIW, the typical residential design load on a floor is 50psi, with 10# being dead (constant which includes the subfloor and any finish materials on it) load and 40# being transient load (like the people and water in the tub). Some bathrooms are built with it higher. But, a typical home handles a tub fine, even if it does exceed the design load by a bit. It may become a bigger issue if you then want to use lots of ceramic or stone in there unless it was designed for it.
I've not looked at Kohler's installation instructions, but most call for a ledger board to help keep the tub from rocking or shifting. Once the walls are up, it is hard for it to move much. The ledger helps when you may say sit on an edge - if installed correctly, it will help prevent it from rocking onto two legs. If this tub is being used as a shower, and you have drywall up in there, you do have a problem, though, especially at this stage. If it's only a soaking tub, it may be okay, but is still not ideal.
MOrtar is often used underneath a tub - it's more important on non-CI tubs (like fiberglass, and acrylic), to help support the bottom from flexing. It can also be used to help level. If used, regardless of the material, it prevents the tub feet from sinking into the subfloor because it spreads the load out much further.
Keep in mind that deflection is critical not only along the joists, but in between them as well (from the subflooring). Depending on the type and thickness of the subflooring, excessive weight on an individual tub foot, particularly when it doesn't have the ledger boards to prevent it from sinking, it could be an issue.
Maybe a few pictures would help suggest a solution to your situation for others to comment.