Jemima Murray was your 'very great' Aunt of course, however I do not have your ancestry line and cannot see if you have any mtdna link to her. If your Tiptons were a direct line to her husband then of course you would all be genetically linked. According to what you have told me however it seems that you are laterally genetically aligned with your 'Vgreat uncle' Tipton as it appears that his brother was related to you directly.
As your surname is not Tipton however you would not have a Tipton yDNA profile, however you would certainly have the Simmons profile if your father was a Simmons.You might be interested in exploring that line via yDNA testing, the y67 test is the best, however y37 would suffice. yDNA lines test your direct paternal male ancestor line only.
There is also a Family Finder test for about $299 which is the most expensive test and finds lateral line descendants as well, FTDNA include a y12 DNA test as well in that (or mtdna, depending if the client is male or female.
You can read all about that on the family tree dna site: https://www.familytreedna.com/
Our Murray surname site link is below herewith.
Have you looked at Brent's research on www.familysearch.org as yet regarding the Murray Morgan marriages & lineage?
Perhaps you should try and get in touch with him, I shall look for an email address.