Transparent monitors mark nodes down

As I read this and look at your diagram, it does not make sense to use a transparent monitor in your setup. It would make sense only if you put a destination IP that is outside of your network and must be reached using one of the routers.

Lets, for example, say you Put 203.0.113.100 in the destination.

The way this works is you should put the IP address that you want the monitor probe to be sent to as the value of Destination. In your example network lets put 203.0.113.100. The monitor will then send its probe to 203.0.113.100 via whatever routing you have set up. In your example, it will use routers 10.10.10.1 or 20.20.20.1. It will use the layer two address to send the traffic to the next hop router to be forwarded to the destination. This is designed to verify that your routers are working properly and are able to forward traffic out to the destination 203.0.113.100 via the routers. It is really monitoring the routers, not the destination.