The matches are done at the lab where the DNA sample was sent to.
Wikitree itself does not do any DNA matching. Wikitree simply links to profiles that the original DNA test taker MAY be related to. It can take up to 24 hours for that DNA info to be propagated through the system.
For any profiles that you may be related to, and for which you are not the profile manager, you can contact the profile manager and see if there is any connection between you and them - are they also related to that the person whose profile you are asking about.
Most of your DNA matches should be done through the company that tested your DNA - such as Ancestry, 23&me, My Heritage, FT DNA and Living DNA in the UK.