In Shulchan Aruch Kuf-peh-gimmel seif bet its written that the kos of bircat hamazon should be washed and pour wine inside and at the 2nd bracha to add water (i think “limzog” is the word) ;
in Ben Ish Hai pasrhat shelach , shanna alef, halacha yud-chet Rav Yosef Hayyim writes the same thing
1. Should one first put the cup down and the one who was holding it pours water? Or is it someone else at the table pours water for him while he holds it a tefach above the table?
2. When one pours water would this be poured in three pourings like the Ben Ish Hai wries elsewhere for kiddush?
The original idea of pouring water into the kos was to make the wine drinakable and superior. The wines of Chazal were strong, and water needed to be added. To express praise of the Land, the final addition of water was made at Birkas Ha’aretz.
Today, our wines do not need any addition of water, and therefore Rema (183:2) rules that there is no longer a need to do this.
Nonetheless, some continue to add water to the kos, because of kabbalistic reasons.
One who wishes to do so need only add some drops of water. Usually, when making a berachah on the kos somebody else is there (the common custom is to make birkas hamazon on a kos when there is a mezuman), and therefore the simplest way of adding water is by somebody else pouring it in.