how big is your hand?! I think it's only a plus if you can wrap your hand that easily around the neck

you use your thumb only to give a counterweight/counterpoint to your fingers, in order to be able to use your fingers to give enough pressure on the fretboard, meaning you put your thumb wherever feels right (ok some use their thumb for the low e-string or mute the low e-string but that's a whole other thing)

I have no idea how you use your thumb though, maybe you can upload a picture :)