Why do I keep finding items in Dark Rooms past the amount shown in the counters?

Dark room completion items found in the premium regions are shared among all three rooms in that region. Additionally, they are capped at the total number required to finish the zone. For example, Versailles requires 7+9+10=26 total of each item to complete all three dark rooms. You'll continue to find items up to the cap, and they carry over to the next sites!