The most likely explanation is degrees of separation. The daughter never took a test but one of her children probably did, which would also carry evidence of his DNA.

EDIT: also, just because she says she never took a DNA test doesnt mean her DNA has never been tested. DNA tests are not new, easy-access tests are.

The article is confusingly written so it's hard to figure out entirely, but obviously her records, or someone already linked to her were in the database.

DNA analysis and the databases are so well populated at this point that they can often "find" missing people via gaps.

Here's an anecdote - In my family an unknown person did a test which connected her to my family, people who already took the test. The system said you must be related to these people. Now my father also took a test but didn't give his personal information, so the system knew both my extended family AND that this person was downstream of my Father specifically but didn't know who he was or how to reach him. She was able to contact other extended family who said my father had the following children, one of them must be your biological parent. The woman was able to easily look at ages and genders at this point and identify her missing biological parent who wasn't in the system at all. Low and behold through the miracle of Social Media, this person got that "Hi, I'm your adult child" phone call.

Unfortunately the story doesn’t go into detail on who the “two boys and a girl” are, so I can only assume that they are Melissa/Melanie’s children. If one of them took a DNA test, it would show DNA matches. The story just doesn’t say where that information came from.

Without testing, you would have no idea. So there must have been someone down that family line that was tested.

Edit: you could always hop over to Twitter and ask the reporter for clarification

There are two things these sites do: DNA sequencing and genealogy.

Genealogy is a big field. Lots of people, both professional and hobbyist, spend hours combing over public records or walking through graveyards, taking careful notes. They build very detailed records of who is related to who based on these records.

But those records are often incomplete. Sometimes the father isn't reported at birth. Some children are born in secret and not recorded. Sometimes birth records are falsified. Genealogists ALSO try to figure that stuff out. Sometimes people who find out their parents weren't biological hire detectives to try and put together where they came from. If that gets back to a genealogist that can help them piece together more accurate records. (I had this happen, I found out when I was around 19 that certain aspects of my family tree were lies to cover up some things a different family member was too embarrassed to admit.)

The most extreme cases are things like the fertility doctor who was using his own sperm on patients instead of the donors they had selected. There are dozens of people we know have incorrect biological lineage because of him, and we're not 100% sure how many more there might be because he wasn't consistent and even he can't remember every time he did it.

DNA sequencing helps do that. If it finds a close match, some detective work might reveal there was a birth that wasn't reported properly. Sometimes it's just coincidence. Sometimes the people who know the truth all dead. But generally if people match enough and have parents who were geographically near each other roughly 9 months before their birthday it's not a stretch to assume there might've been a misreported birth.