Pretty self explanatory. Some say at chatzot all week and some in the morning. Why davka on the first night does everyone say at night? This minhag does not seem apply on the second Saturday night (when there is one) or on Motzaei Shabbat Shuva. Sources always appreciated. Thanks
Because it has a slicha begining with "Bmotzei Mnucha" (At the end of the day of rest) and we can't say slichos and 13 midos before midnight.
The source mentions Magen Avraham 525:5 which cannot be true (there is no such sif katan 525:5, and in general this siman is about borrowing on Yom Tov). Most likely it is referring to http://hebrewbooks.org/pdfpager.aspx?req=14327&st=&pgnum=301 (581:1)
Although most places I know of do say it at Chatzos on the first night only, I do know of places that say it every night at Chatzos, and I do know of places that even the first night say it at 5:30 AM. I have heard from my rabbi that the reason many people say it the first night at Chatzos is because Zerizin Makdimin L'Mitzvos, and as the Magen Avraham 565:5 says the earliest time for Selichos is at midnight. The reason it is not done by most people the rest of the week is since practically it is a difficult time as most people are sleeping then.