So far no errors, below I’m summarizing the changes I have done to and the error disappeared.
Old Setup with errors “file being used by another process”;
Veeam Backup Server was having three interfaces, one 172.16.30.66 where it communicate to vSphere Management Network, one it communicate to iSCSI Initiator on 10.10.10.66 and one Production 192.168.10.60 where it is joined to the production domain.
Proxies was added to the Veeam via 10.10.10.x network for sake of segregating the network traffic. Also repositories were added via 10.10.10.x network.
In this configuration, it seems the Veeam Server communicate with vCenter via the vSphere Management Network, and assigning the job to one of the proxy which is added to veeam server via 10.10.10.x network.. Repository added to the veeam via the vSphere Management Network.. Now, here I think the dilemma where the error being generated. Veeam Pulling VM info within the job from different interfaces, proxy communicate to veeam via different interfaces and job being off-loaded to disk via different interfaces. Plus, the iSCSI Initiator connecting to the Repository Target via same interfaces where it’s added to the Veeam Backup Server.
After the changed as per the attached diagram;

Veeam Backup Server has two interfaces 172.16.30.66 and Production where it’s joined to the production domain on 192.168.10.60. vCenter added to Veeam via 172.16.30.0 network as it’s set on a separate management interfaces.
Proxies and Repositories added to Veeam via the vSphere Management Network where Veeam communicate with vCenter via same Network. Repositories accessing the Repositories LUNs only via the iSCSI Network on 10.10.10.x.
Proxies set as a HotAdd mode and Jobs set as Automatically. All jobs running successfully now without any error and faster via HotAdd Mode.