All reported posts go into a mod-only forum called "Unclaimed". All mods get a notice in their notifications when a reported post lands there. Often, more than one mod has seen the report and they act on it simultaneously. Once a mod has spam hammered the perp, they go and move the reported post from "Unclaimed" to "Closed". Depending on the reported post, a Mod might move it to "Claimed" or "Problem Users". Why the different folders? Well, some reported posts are so obvious that we don't need to discuss them. There's nothing to discuss when it comes to a spammer. We click our Spam button which reports them to "Stop Forum Spam", bans there IP address, the spammer, and deletes all of their posts. It also shows us similar posts and other peeps who post from that IP.
However, some reported posts aren't so obvious. We discuss those, and a mod will ultimately "claim" it, move it to the Claimed folder, and while we all can still chime in, they get to make the final decision on our action. Often, we notify the reporter of our action(s)m but not always. It can be a lot of work to clean up a thread, rather than delete it. Same with posts, and there are many mods opposed to editing a problematic thread, so they just delete it.
Often mods will recuse themselves from chiming in when there is a conflict of interest or even a perceived conflict of interest. That includes already being in that thread, having a personality conflict with the poster, etc, etc.