Bathtub Floor Support
In order to determine the adequacy of the 2x10's, you need to know the clear span of the 2x10's. Also need to know any additional load in the bathroom that they will be supporting. Clear span means the distance between supports for the 2x10's. The plywood is typically ignored in computing the bending capacity of the joists, however the plywood is important in preventing lateral buckling of the joists.
There are two possible cases to examine with respect to the ledgers of the tub. In case 1, the ledgers are perpendicular to the joists, in which case the tub acts as a series of point loads on the joists. In case two, the ledgers are parallel to the joists. If the ledgers line up with the joists, then the tub acts as a distributed load over the joists. If the ledgers do not line up over the joists, then the ledgers act as distributed loads over the plywood, and you need to determine two things, first if the plywood is sufficiently strong to carry the load, and second if the joists are sufficiently strong to carry the load. The load on the plywood depends on how far from the joists the ledger is.
The manufacturers recommendation of 49 psf is a simplified approximation, which does not account for the point load action of the tub if it is perpendicular to the joists, or the bending on the plywood if the ledgers are offset from the joists. You may want to have a structural engineer look at your particular setup, as I doubt the manufacturer will assume liability for the structural support of your house if the joists crack, regardless of the psf capacity of the floor.