OK, thanks.
In my case the problem is that I can only run the job every 30 m, which is frankly too much for "instant messenging"...
No way to trigger the job...
Update: the notifications actually arrive, but with a very long delay (say one hour).Not sure it's a CjForum or Joomla! issue though (reply notifications are sent...
However, now I cannot receive email notifications of PM (checked spam, spf et c. I assume the mail sender is the standard Joomla! one).
I enabled the options and tried...