The FETs activate when their gate voltage, relative to the source, is sufficiently above the gate threshold voltage. (The threshold voltage is specified for a very small drain current, such as 250 µA; here, we need more current for the pull-up resistors. The gate voltage we want is the one for which the datasheet specifies RDS(on).)
The low-voltage side can activate the FETs by driving low the source.
The high-voltage side can activate the FETs by driving low the source through the body diode, which adds about 0.7 V.
So this circuit will work with a gate voltage of 2.5 V as long as the FETs fully switch on at 1.8 V.