An iOS device when connected to Wi-Fi with proxy enabled cannot receive notifications from Apple Push Notification service (APNs). This is because APNs requires a direct and persistent connection from the device to the server. Hence, the TMMS iOS client cannot get any notifications from the server resulting in the "Out of Sync" status displayed on the server's web console.

If you want to use TMMS to manage your iOS device, make sure that the iOS device is directly connected to the APNS server, not from the proxy server. For more information regarding APNs, you may refer to this Apple support article: Unable to use Apple Push Notification service (APNs).