If your IT service provider has set up your firewall in a way that does not allow IMAP or POP3 traffic, by default, then you will not be able to receive notifications from your YouTrack InCloud instance. To solve the problem, the IT provider should know a range of IP addresses, from which connections to IMAP/POP3 will be coming, to create required rules in the firewall to allow that traffic, only.
To watch for updates in available IP ranges, please, keep an eye on Amazon EC2 Public IP Ranges announcements in the AWS Developer forums: Amazon Elastic Compute Cloud. YouTrack InCloud uses servers in "US West (Northern California)" and "EU (Ireland)". Thus, you should refer for the related sections of the latest announcement: Amazon EC2 Public IP Ranges.