Miles's continuity is adapted into the current one.
Considering what Peter saw at the end of Spider-men when he googled Miles, this could be that forgotten plot thread so where in new continuity Peter discovers current Miles and decides to train him.
Miles was also surprised to see his mom at the end of Ultimate end, so the two continuities smashed together could mean that the Ultimate universe timeline is still his history, but he now has memories of growing up in this universe. He is still the same Miles as before but has been adapted into the new universe so he has a second history here.
Imagine if you will, you woke up in a new life but could remember enough of the old one that you are still you but have been living life over in this one. This is just a plot point yet to be explored. Miles dealing with the knowledge of living two lives would be kind of hard to take in. Like people you knew before that had been dead are now alive, or your loved ones are different things entirely or dead or nowhere to be found. He may just be embracing his new history just to try and stay sane.
Miles having his friends & family with him on Earth Prime is the only thing that's keeping him from loosing it. Look what happened to the Squadron Supreme.
Peter has nothing to teacher miles, considering spider totems are self taught warriors with thier own spin on things. Miles has proven better and more naturally versatile than Peter in spidermen.