When you get attacked by the DB totally and completely depends on which game you have. If you have vanilla Morrowind, they will attack you almost immediately. I have gone directly to Caius Cosade's place and slept in his bed and have them attack me. If you DON'T want to be attacked at all, then just sleep in the woods way out of town. I have never been attacked by the DB unless I was sleeping in a town.
Now if you have the GOTY version of the game, whether for the Box or PC, you will NOT get attacked until you reach level 6. This was done because, let's face facts, those Adamantium swords with paralyze on them are NO laughing matter at level 1. Neither are the Carved Ebony Dart's.
Also remember that you HAVE to have either one of the DB Helms or one of the Ebony Darts to 'prove' to Apelles Matius that you have been attacked by the DB. If you have neither, he won't believe you and won't give you the Guild Guide's name.
You will get attacked up to, but not to exceed 9 times. That does not mean that you WILL get attacked 9 times, it simply means that you COULD be. My newest character is a Spearman Argonian(Treads Softly, but carries a big Spear) and he has only been attacked twice and he's at least level 20.
I might be wrong, but I think that once you show the helm/dart to Apelles Matius in Ebonheart, the attacks stop. That is the only explanation that I can come up with. The only one that fits anyway. ;o)