Having the same issue
I'm having a similar issue:
Autoresponder is working and the customer is getting an email. :)
For 'New Ticket Alerts' the admin account is getting mail but the support manager is not.
New message alert also does not appear to be working for assigned staff.
My settings for alerts in settings/preference/alerts appear to be correct:
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New Ticket Alert: (Enable) Disable
Select recipients:
(tick) Admin Email (tick) Department Manager Department Members (spammy)
New Message Alert: Enable Disable
(tick) Last Respondent (tick) Assigned Staff Department Manager (spammy)
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osTicket 1.6.0
Using a direct pipe to pipe.php for incoming / SMTP for outgoing