As discussed here, while doing Kiddush Levanah, we say "Shalom Aleichem" to 3 other people, and they respond back with "Aleichem Shalom". I've seen some people saying "Aleichem Shalom" together with the person responding to their "Sholom Aleichem".
Is this a custom? Is there a source for it? I didn't see anything written about it in the Siddur.
http://hebrewbooks.org/pdfpager.aspx?req=7167&st=&pgnum=56
The Sefer Zohar HaLevana explains that the reason we say Shalom Aleichem and then say Aleichem Shalom together, is that the first day Eliyahu Hanavi comes to announce the coming of Moshiach (three days before Moshiach comes), he will say "Shalom Ba L'olam, Shalom Ba L'olam". Therefore, after we say "Dovid Melech Yisroel..." (which refers to Moshiach) we also say Shalom twice, in the form of "Shalom Aleichem, Aleichem Shalom". [and if so, why do we not say it before "Dovid Melech..."? Because real peace will only come once Moshiach comes.]
Also, Zvi Ron quotes 16th Century Kabbalist R' Hertz as follows (see page 246 footnote 26):
after praying for the coming of the Messiah by saying ‘David, King of Israel, is alive and enduring,’ “since the birth pangs of the Messiah are many, it is incumbent upon us to pray and say each person to his friend ‘Shalom Aleichem, Aleichem Shalom.’ ”
There are a few different customs. I asked 2 different Rabbanim about this after noticing that my Siddur said to say "Shalom Aleichem" to 1 person 3 times and not finding a satisfactory explanation for the difference in the Tur, Shulchan Aruch or Mishna Berura. One of the Rabbanim came back a few weeks later and told me the following: (He said he looked in a Sefer that explained different Minhagim but I don't recall what the name was.)
There are 2 different Minhagim in regards to "Shalom Aleichem"in Kiddush Levana, both of which are valid. The most common practice is to say it 1 time to 3 different people, which makes sense as this is the normal way to greet people. The other Minhag is to say "Shalom Aleichem" three times to one person. Incidentally I recall listening to a pre-recorded Shiur on YUTorah.org in which Rav Schachter said the 2nd Minhag was Rav Soloveitchik ZT"L's custom.
As to what you saw, that wasn't mentioned. If it is a Minhag, it must be rooted in a desire to say every word, but a concern for Shome'a K'Oneh, meaning that if someone simply answers "Aleichem Shalom", they've essentially said "Shalom Aleichem" to however many people prior to saying it themselves. I don't know if that applies to Kiddush Levana or not though.
As a total side point, if you look in the Artscroll Siddur with the English, it says to say "Shalom Aleichem" once to 3 people. The Hebrew Siddurim says the inverse - 3x to 1 person. This is the true for both Nusach Ashkenaz and Sefard - I checked.
