I know, it's because I'm trying to re-create your steps in search of a convenient work flow I might adapt. As closely as I can determine you took the following steps:
1. Looked at Dodd-718 page to see the test-takers. (and this is already a starting point I don't have, since I don't generally know any profiles that list my test, other than the ones I entered myself and thus already know.)
2. Selected A825728 on that list.
3. Found Vincent's profile, or maybe went to his test on the list there on Dodd-718 page, clicked on the test to do a one-to-one compare, finding the shared segment on chromosome 14.
4. Did a relationship finder from either Vincent's profile or Dodd-718 profile to reveal 4th cousin relationship (not sure this is needed, but it's information)
4. Did a matching segment search on Vincent's gedmatch, to find other triangulating segments.
5. Searched for those segments on Vincent's one-to-many report (this is the part where I thought the segments didn't appear there when I ran them earlier, although on running it again just now I did find them - in my own example matches, the triangulating segments weren't on the one to many so I had to search for them on wikitree) and determined there were no wiki links there.
Then invite them - and then you want to the next test, where you suggested he invite the match to make his profile public to determine the relationship. Was there a reason you didn't go on to repeat the search for matching segments there, to invite to wikitree.
Again, just trying to understand what I might do to make use of my DNA on wikitree, because right now it's now doing anything for me that I can see.