But how do you equate 'strange things happening' to the 'twilight zone?" Could it be that the day transitions from light to dark during the twilight, so in an analogous way one could say things that are normal can turn to being strange -- as you enter the twilight zone? Actually Cambridge had the following definition:
The twilight Zone was a TV series (and also a movie) that featured mild horror stories, usually about unsuspecting 'average Joes' ending up in strange situations.
Among Americans of a certain age, just whistling or humming the opening bars of the theme music from the TV series means "something really weird is going on here!" The TV episodes usually involved a situation that started off very normally and then took a surrealistic turn.
I'll try to post a link to the music, but I'm not sure it will work... go here and click on Disc 2: Main Title, Sec