I'm not to sure really, but I can recall 2 years ago I saw a 9 pointer chasing a doe all over the woods one afternoon. This was October 3rd.
Shot the guy about a month later
As far as the mini-rut and the famous october lull well I don't really know. I hunt harder the first 2 weeks of October than I do towards the later part of the month. Most of this is just because I am trying to stockpile hours at work so I can sneak out a few days during November.
When it comes to a mini rut I tend to believe that there is another (smaller) round of does that are being bred into the first part of December. I have seen a mature (4.5 yr. old) bedded up with a doe as late as December 16th.
I don't let these sightings change my way of hunting during these periods. In early season/late season I am still focused on feeding sources.