Firmware is updated automatically overnight when the network is not busy. You cannot update the firmware manually through the Plume Home app.
Checking the installed firmware version
Open the Network page and scroll down to the Extenders section of the Connectivity tab.
Tap on the tile of any of the extenders shown.
Tap the corresponding View details button of the extender you want to check.
The firmware version will be at the top along with additional information about the extender, such as the serial number, MAC addresses, and IPs.