On a quick read of the Millennium Report a couple of days ago, I got the impression that nothing really 'triggers' the Hammer, HAMR. The operator inputs an identifier (phone number, IP address, bank account number, email address, credit card number, tax ID, etc.) and date range, and all the electronic metadata on that identifier over the date range is returned.
This then can tell the operator information such as travel map, phone contacts, bank transactions, stores visited, toll booths, web sites visited, email contacts, etc. that occurred over that date interval. It is a very powerful snooping tool.