I usually just leave everyone the way they are when they are plague stricken. No need to move them out. If you do, just don't move em in again is all.
As for black death, once you get the warning, move all generals (agents too actually) out of the town (like 1 square out) and have them wait till the plague in their town is over. Don't worry about riots as those will die down with plague. Also, some settlements are never affected by the black death. Arguin and Edinburgh and 2 others.