In fact it does work.
It tested it several times works like a charm.

Just configuration may be weird.
Have a look at global parameters how to configure imap to read replies, it works the sae way.

NB : if you want help, please give more information than just "seems not working"

I have setup the IMAP host and user under Controls & Automation -> Input mailbox for Tickets

Under Global parameter -> Automation

IMAP host: {myhost:993/imap/ssl}INBOX

Also tried

IMAP host: {myhost:143/imap}INBOX

(NOTE: you been referring us to user manual but it is not anywhere in the user manual)

Admin Cron is running.

telnet myhost 143

Result: *OK Dovcot ready

When is send email to support@mywebsite.com, I receive the email but it doesn't to Work -> Tickets

Where could be the problem.

Possibly you read the email from a mail client.
ProjeQtOr will only treat unread emails (to avoid treating same emails several times).

It email is correctly read, you'll have some trace on the mailboix definition and in the logs.