Wikitree doesn't store or collect any actual DNA information, so the "DNA connections" you see are people who have taken DNA tests elsewhere and who, according to the profiles and connections here on Wikitree, are likely to share some DNA with the profiled person and perhaps with you as well. You need to do an actual comparison on a third-party site like Gedmatch to find out if you actually share any DNA.
As far as marking a relationship "Confirmed with DNA" you can confirm a relationship without actually having DNA from that person. For example, if both you and a sibling have tested, the test shows that you are full siblings, and you have documentation (such as birth certificates) that names your parents, you can mark them as "confirmed with DNA" after adding a statement something like
- Paternal and Maternal relationships are both confirmed by an autosomal [name of test] match between [you] and [your sibling]. Their most-recent common ancestors are [your father] and [your mother] the parents of both [you] and [your sibling] Predicted relationship from AncestryDNA: Sibling, based on sharing [xxx] cM across [xx] segments.
You can confirm other more distant relationships by matching DNA with first, second, or third cousins. Here's a link to the Help page for Confirming with DNA:
Help:DNA Confirmation (wikitree.com)