Subfloor and underlayments are always installed with the face grain perpendicular the joists, never with them. Whoever installed yours goofed and so the space between the joists has more bounce than it otherwise would have.
Be sure to leave 1/8" gap between the new sheets, 1/4" at the perimeter and at all solid objects and fasten into the subfloor with 1 1/4" floor screws avoiding the joists. Of course stagger the seams from the old by about 2' or so.
Don't forget the mandatory thin set under the Hardie, proper fasteners and mesh tape for the seams.
Have you evaluated the stiffness of the joists' yet to make sure they're good enough for tile installation?
OOOPs, It would have been better if you had added this question to your other thread since it's the same project. That way we would have seen that this is an attic room and would have seen the other info and comments.
Being an attic it's likely that the joists are not as the main living space. Was probably unfinished and the homeowner just threw down the sheets. (wrong). Wouldn't surprise me if the area was just an attic, the joists may be 2x6", have you checked that?
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