Dovecot exactly conforms to RFC 3501 Section 7.3.2 where the \Recent flag
for new messages may only be sent to one session if multiple sessions of a single user are active. The current implementation of the open-xchange-push-imapidle is just looking at the \Recent flag, though.

A new option will be introduced in /opt/open-xchange/etc/groupware/push_imapidle.properties:

# when to fire push events?
# possible values: newmail always
# default: always
com.openexchange.push.imapidle.pushmode=always

When set to always, which is the new default, there will also be push
events when any other change to the mailbox is done e.g. deleting
a message or changing other flags.

Possible side effects:
If users are concurrently using EAS, Outlook OXtender2, the open-xchange webui or any other imap client, many more push events will be triggered.
To get back the old behaviour, set

com.openexchange.push.imapidle.pushmode=newmail