Answer: Foxhound does not actually issue Alert #1 right away, it waits for at least one minute (or whatever the Alert #1 criteria has been set to) after Foxhound is started.

Here is an example where it looks like the Alert #1 was issued right after the "Foxhound stopped" period ended. However, the timestamps show that the "Foxhound stopped" period ended at 6:53:15 AM but the Alert #1 wasn't issued until 6:55:26 AM:

6:55:39 AM   8.1s  .1s / .1s  2  ...
6:55:36 AM   ALL CLEAR - Alert #1: Foxhound has been unable to gather samples for 1m or longer.
6:55:31 AM   2m 16.2s  .1s / .1s  2  ...
6:55:26 AM   Alert #1: Foxhound has been unable to gather samples for 1m or longer.
6:53:15 AM   27.5s      -- Foxhound stopped --
6:52:47 AM   1h 6m 41s  -- Foxhound stopped at --

See also...
The Alerts Criteria Page