Yep, some of those strings go under, not over. In fact it's always, over, under, over, under.
He he. Still, you only need to correct a few string, maybe not start all over.
I think what has happened is that some strings cross on the tiles, rather than just between them. The Rubik's tiles have too many grooves anyhow. If they only had one set of parallel grooves rather than that crosshatching, you'd never make this mistake. Some magic knock-offs have this.
If the incorrect strings are underneath some others, it can be difficult to extract them without taking correct ones off.