I don't rememer this from my previous play throughs, but after resting in a cave, an assassin came after me. I dispatched him, and searched his corps. Lo and behold, he was decked out in Dark Brotherhood gear! I'm still level 2, wearing chitin armor. This DB gear is about 3 times as good as my current stuff. Is this supposed to happen?

I have Tribunal and Bloodmoon installed, if that matters.

They come after you if you have Tribunal installed, doesn't matter what level you are.

If you're on PC, you can apply a mod that will not trigger the attack until you're after particular point in main quest (so you are quite widely known person).
As for the gear, yea it's overpowered for a starter. I think that when they released Tribunal, they thought that most people will already be high levels. If you do not wan to play "overpowered", you can sell it, store it, etc.