Samantha has the correct answer. When a profile is created, if the four-tilde signature is added to the initial biography box or comment field, it's simply stored as plain text, i.e., just as ~~~~. But when the profile (individual or FreeSpace) is edited, any instances of four-tildes are converted and saved.
In other words, at initial profile creation, no convert/replace happens; at each subsequent edit, it does. It's a WikiText (as in MediaWiki) thing, not exclusively a WikiTree thing. So if ~~~~ is entered at profile creation and not later deleted in an edit, the next edit-and-save will cause the four-tildes to be changed to the current date/time signature. Once the edit-and-save has happened, the signature is saved as its full WikiText string, for example: [[Williams-49144|Williams-49144]] 21:12, 11 July 2021 (UTC). Any following use of the edit function will show that in the biography box, not the four tildes.
If a profile editor didn't know what the four tildes were and just left them there, then they would be converted and stored as the editor's profile link and date/time stamp.