No, upgrading the firmware of a storage controller does not also upgrade the firmware of the attached disks. That would be a separate process.
Kindly suggest me on how to get the firmware/driver versions of the disks on the esxi hosts ?
I have got the firmware/driver version of controllers, but could not get information on how to get the same for the disks.
You're going to have to contact either your server vendor or the disk manufacturer.
The Firmware in use for each device should be identifiable from the 'Revision' entry from this information (provided the disks are passthrough):
# esxcli storage core device list
Alternatively (whether they are passthrough or RAIDed) you should be able to see this information in the out of band management console (e.g. iLO, iDRAC) of the hosts.