EDITED: I misread your original post as having an original tip size of 0.001 inches!
I don't think so You don't say which station you have. But if the station is expecting 0.01 in per tip, but it is now registering 1 mm per tip (are you *really* sure it is 1 mm, not 0.1 mm?), Then ideally you need to do the correction in the station itself. Or at least some of the correction.
If all the correction is being done in CMX, then the multiplier would be 3.937008.
In this part of the world a 1mm per tip sensor would not register any rain on many days it rained less than 1 mm.