This sounds like a case of the “Old Hag” phenomenon. There is a big topic about it here, although it hasn’t been updated in a while.
When your body is in a state between wakefulness/sleep, it’s not uncommon to hallucinate, especially if you’re in SP. The “Old Hag” refers to a situation in which you’re in SP, and you see or otherwise sense some type of figure (an old woman, a monster, a hitman, etc) sometimes accompanied by a sense of fear. I’m sure there are better definitions, but that is my understanding of it 
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Since you were just dreaming about being pursued, it makes sense that that is what you would see. It can be scary, but just try to remember that it’s not real. Hope this helps!