Someone recently sent me a C&D for a domain I have owned for over a year and a half. I researched their portfolio and they use MarkMonitor, so I don't believe it tells them right away. My guess is that they would download daily zone files and perform a search for their trademark.
MarkMonitor may perform the same options for them, but that is how I would do it if I owned a trademark and wanted to know who registered new names.
I've received several C&D's the last month, 1 appears to be real and a few others were fake, so do your research before you hand over any domains.