Your question is based on the wording of the Rambam (Hilchos Parah Adumah 15:1) that "if he sprinkled onto the person who is Tamei, the water [that was sprinkled] remains Tahor."

However, we understood his words to be Lav Davka, and the water is Tahor even before it is sprinkled on the person who is Tamei, from the time that the Ezov was immersed for the sake of doing the Haza'ah. Our reasons for learning the Rambam in this way were as follows:

(a) The Rambam adds "and so, too, the water that was splattered at the time of the Haza'ah onto the earth...." Such water never touched the person who is Tamei and thus it cannot be said that it was effectively used for Haza'ah, and nonetheless it is called "Na'aseh Mitzvaso."

(b) The Rambam writes further that "when one immersed the Ezov in order to do Haza'ah on something which is not Mekabel Tum'ah, the water that drips off... will be Metamei because the Mitzvah was not done with it, since the Tevilah was done for the sake of something which cannot be Mekabel Tum'ah." The implication from here is that if the Ezov was immersed for something which is Mekabel Tum'ah, then immediately upon the Tevilah the water is considered "Na'aseh Mitzvaso," and the water that drips off is Tahor. (It is clear that his intention there is to explain the Mishnah cited in our Sugya, and therefore he is certainly referring to a case where the water was not yet sprinkled on the person who is Tahor.)

M. Kornfeld