How does this under voltage lockout (UVLO) work?
Well, it doesn't properly work because there is a connection missing. Look closely at the drain of the right-hand MOSFET - there is a black dot that signifies another connection but, that connection is missing: -

Without that connection (I've added it in red dotted lines) the whole right hand side of the circuit is pointless because it doesn't activate or deactivate anything.