Heard back from my inquiry to the Salvation Army Divisional Museum:
"I am sorry but we are not able to find information regarding your Great Grandfather Joseph Milburn. We do have records on people who became Salvation Army Officers but not members (soldiers). I think Mystic was an Outpost connected with the Corps in Centerville. Some Outposts grow and become full-fledged corps and others do not. I am glad Joseph joined the United Brethren Church when The Salvation Army was no longer in Mystic. I would be interested If you find any other historic information regarding Joseph Milburn.
Historical Museum Director"
I had also called the closest church in Ottumwa, Iowa as well as Omaha, Nebraska, but no luck. This effort has reached a dead end, I'm afraid.