What did they do when you saw them?

I didn't. I don't particularly have to go out of my way to find Twilight fans, but if I did, I wouldn't.

How do we distinguish the difference between the kind of fanaticism that mentally unbalanced people display for, say, a show that is considered by many to have unhealthy themes and the kind of excitement that normal people display for the things they love? Maybe Twilight isn't the best example here.

I think you're dramatically overestimating the degree to which fans of Twilight are psychologically abnormal. Harlequin romance was already an incredibly popular genre known for having unhealthy themes. Twilight, like Eragon, is a mostly typical work of its genre with a few distinguishing factors which sufficed to garner it extra attention, which expanded to the point of explosive popularity as it started drawing in people who weren't already regular consumers of the genre.