No, no. The care instructions are for "washing the batting right out of the package, before layering it into a quilt.
The hand agitating doesn't have to be done that way either. I've used Hobbs batting for years and all I've ever done is fill the machine with cool water, stop the cycle, push the batting up and down a few times to make sure it is thoroughly wet, let it sit 5-15 minutes, drain and spin the water out without allowing any agitating, and then "air dry" in the dryer about 15 minutes, then drape it over a drying rack, sofa, whatever for the rest of the evening.
I like the shrinking, wrinkly texture of quilts after they are washed, and doing this to a Hobbs cotton batting before washing the whole quilt, still allows that look.
Jan in VA