I had a test to check an all seems allright.
I created 1 project P with billing mode "on caped produced work", affect 1 resource R, add 1 activity A with 12 days of validated work, and assign 10 days for A to R.
Then define activitty price X.
Enter 5 days of real work on A for R on august.
Create Bill B1, add line for R on X on august (1 to 31).
Enter 3 days of real work on A for R on september.
Create Bill B2, add line for R on X on september(1 to 30).
Enter 4 days of real work on A for R on october.
Create Bill B3, add line for R on X on october (1 to 31).
As 7 days have already been billed, billable is only 3 (10 assigned - 7 already billed), so I cannot bill the 4 worked days but only 3. Capped is OK.