Understanding Distances with Mob Switches

I'm working on a nether mob switch for my small server. The render distance is set to 20, and the simulation distance is set to 10. I currently have 70 zombie villagers in a box for my switch. (There are a few other mobs listed as existing, but they must be persistent for one reason or another.)

As I move away from the mob switch, my mob cap stays locked at 70 mobs. It is not until I get to 23 chunks south of the zombie villagers that my mob cap opens for other mobs to spawn. Doing that to get 70 new mobs and then moving back one block moves my hostile mobs temporarily to 140 until others despawn.

I thought that the limit for a mob switch to work was the simulation distance on the server. Since we have a simulation distance of 10, that should be an area of 21x21 chunks centered on the player. However, it seems that the render distance is keeping the mobs loaded. My guess as to why it is 22 chunks instead of 20 is that there are two borders of lazy chunks around what the render distance is keeping loaded. Is this how it works?