How do they communicate between server and my private network without port forwarding?
Cloud controlled network devices initiate the communication to the cloud. This is the same way that hosts with web browsers communicate with web servers.
If you have a privately addressed network, it uses NAT to communicate with the public Internet. NAT will maintain a table of connections from inside to outside so that any connection initiated from the inside can receive responses from the outside. Port forwarding is really just making a permanent entry in the NAT table, allowing communications to be initiated from the outside.
As a side note, you need to be very, very careful with security and cloud controlled devices. The recent IoT takeover and nefarious use of such devices in a massive DDoS attack demonstrates the problem.