“On”means the systems recognizes these buttons as being pressed, which, as you described, is not correct.
This could be a software (configuration) problem or a hardware problem (wrong pin assignments on the 2×5 pin connector).
To see if this is a software issue I would suggest to test, if using SNESDev works better. For that you
– first need to uninstall the gamecon driver.
– Then you install SNESDev.
Both steps can be done with the RetroPie Setup Script from within the “setup” menu. Just as the gamecon driver SNESDev emulates two game pad devices. The difference is that SNESDev does this in user space (opposed to kernel space). As with the gamecon driver you can use jstest to see if the OS recognizes your gameplay correctly.