Hey, Dan. The info is propagated based solely on the family tree; WikiTree can't look at any of your actual test results. Nightly processing looks at which profiles within a particular lineage state that they have taken a DNA test (and which kind of test), and populates that "DNA Connections" ("It may be possible to confirm family relationships...") on the right-hand side of ancestor profiles accordingly.
With autosomal DNA, that stops at eight relationship degrees (birth events). That means you and 3rd cousins or, in this case, back to 6g-grandparents; 7g-grandparents and more distant won't show your link in the DNA Connections panel.
(Edited to add: That's why your yDNA 67-marker test info does show up on John Edgecomb Jr.'s profile, but not your AncestryDNA test info. And why, by Nicholas Edgecombe, your yDNA test is the only one listed.)