How long does black cap take to yield of results in cockroach population control?

I moved into a new apartment and on the first night I noticed several cockroaches. I’ve been putting black caps around and spraying stuff like raid. I’m seeing fewer roaches, but they say for every one you see, there’s hundreds that you can’t see.

My understanding of black cap is that the roaches bring the poison back to the nest and wipe the nest out. Is that an exaggeration? Does it actually work?