After enable device's DDNS, now we can access the device from internet .How will the device sync. with the AMS to push the data?

It will depend on your setup. If you are connecting the ACTAtek outside the network of AMS, you will need to configure port forwarding to the AMS server. Then after, you can register the ACTAtek to the public IP address of the AMS server.

To register the ACTAtek to AMS, simply login to the ACTAtek's web interface and enable Access Manager mode from Terminal Setup page. Then Access Client Setup page and type in to the end point URL like below.