I just installed Dragonborn DLC, I have a previous character doing the DG quests. She has finished the Way of the Voice quest. Now that I have the Dragonborn installed, will she now be attacked by cultists? In the same manner, will my Dragonborn character also experience vampire attacks since I have DG too? Thanks for your replies...

Yep, and God help you if you're attacked by cultists, vampires, and a dragon in the middle of a city at night. I've had that happen before, and I can't even describe the whirlwind of murder that turned into.