Unlike in the UK, Romania still has a large 'magic' community among muggles. There are white - 'good' - witches, and black - 'bad' - witches, who sell their services to other muggles. Of course, these witches don't have real magic, and the whole thing's based on superstition, but some of them do seem to have real power still. Cristi and Costin's mother was one of these, a witch who practiced both black and white magic and who had a freakishly high success rate, both with her curses and her charms.
All Cristi and Costin have been told about their conception is that they were left on the doorstep by a stork. As far as they're concerned, they have no father, and they're honestly fine with that. Their mother is more than enough, in their opinion. Raised in a house full of magic, the twins were taught everything their mother knew growing up - how to read tarot, tea leaves and crystal balls, how to cast curses and make love potions.
The thing is, when you live in a country as saturated with magic as Romania is, witches tend to only stay popular for a few years at most, and inevitably they're cast down and replaced by younger witches claiming to be more powerful. Well, that's what happened to Cristi & Costin's mother, and in order to continue practicing witchcraft she moved the whole family to England, where there was much less competition. But not before cursing every single person who betrayed her in Romania.
So, aged seven, the twins accompanied their mother to London, to settle among the large Romanian community there. Their mother lost popularity with no customers, despite the growing Romanian population in the heart of London; so, she began using her curses on bigger projects. She often cursed politicians she doesn't like. Why do you think the leader of UKIP keeps quitting?
Cristi had her first sign of magic before Costin did - she levitated him over a lake because he was annoying her, then dropped him in when their mother caught her. He, however, managed to get out of the lake dry as a bone, and the next day they received their Hogwarts letters.