People are often quite makpid to dry off the netilas yadeim cup and their hands quite well from the start of the process and between the netilah of each hand (i.e. from touching the cup itself, the faucet, etc.) Where does this hakpada come from exactly, what’s the source for all of this.
The source is the Chazon Ish (Orach Chaim 24:20), who writes one must dry one’s hands and the handles, because otherwise when a person touches the water it becomes “tamei,” and ruins the netilah.
The Mishnah Berurah (Biur Halacha 162:2) is lenient concerning these points, the clear reason being that we are not concerned for “tamei water.” The water we use for netilas yadayim is tamei, and after we wash our hands we touch the handles of the keli and the towel (and other things), so that our hands remain entirely tamei, and this is not the point of netilas yadayim.
Rather, the enactment of netilas yadayim, which was made as a decree related to eating terumah, is to perform an act of washing (maaseh netilah), even though we know that this does not actually make our hands tahor.
Despite this, there remain laws of netilah related to tumah, such as not touching somebody else’s hands after washing, and this is the room for stringency of the Chazon Ish. However, it can be suggested that touching hands is different, because this is the specific area that the netilah is due to take care of.