You can start fires by accident. Like knocking over a candle, or tossing a cigarette in the trash.
When I was 9 I threw out a blown out match in a trash bag that had newspaper in it. Burned a hole through the vinyl tile.
I know it's not what Minna said but I can see a jilted, spoiled person doing something in anger and leaving the room and not considering the ramifications.
I think I remember Minna saying, very early on, that one of the prologue characters was still alive in year 90, though very old? Since by then I think Ensi was known to be dead or otherwise gone, I think I had presumed it was Veeti?
The swedish kid (Mia?) makes a lot of sense. We know the family became very wealthy, which means good food and healthcare. The Swedish lineage seems the least touched by the trolls and such.
Otherwise it basically has to be Taru's ancestor (Veeti?)
Emil had tutors, then went to public school for about two years, then joined the Cleansers and served for about two years. Since he was 19 when the first adventure started, that means he was 14 or 15 when he stopped having tutors. He wouldn't have had tutors after the family became poor, so that can't have happened while he was a small child.
One thing to consider is that they didn't necessarily lose everything at once - it's not unlikely they suffered a massive financial blow then continued overspending for a few years.
I imagine tutors would be one of the last things they'd cave on.
So it is possible that the dream is a memory of the day they lost the mansion, and most of their possessions, in a fire - and then they spent a few years trying to believe they were still wealthy before it finally got so bad they had to put Emil in regular school.
It's also possible they tried homeschooling for awhile. Either until realizing they couldn't be bothered - or until realizing how utterly uneducated their son was.