Within every subsequent ten years certainly does not say only once every ten years. On the contrary it leaves the number completely open. With the advent of computers they could run it day and night forever. At least every ten years is what it says.
And how do they relate to enumeration, or counting the population. I'd be all right with your definition if, and that's a big IF, they did what was supposed to happen. Take a count of the population. Not how much your water bill is, or if you have indoor plumbing. Leave those questions for Rasmussen and the like.