Subsequently, the disk on the respective server gets unmounted. However, when we check from ESX, the Network Disk still appears to be mounted. Is there a setting in the API related to this? Where should we check for this?
It's not an API issue. It's how it works with our vPower NFS service by design. This NFS datastore on ESX host you see is kept mounted to make subsequent restores faster by skipping the mounting stage. You can unmount it manually, but it will be remounted on another instant restore or other activity that uses vPower NFS Service. More information here.