The MOSFETs in your diagram have the gate relative to the source, so that's the reference they use. When your gate voltage is 20V, VGS on the left transistor is +10V (20V-10V). VGS on the right MOSFET is 20V (20V-0V) initially, but once current flows, VGS on the right also drops to +10V since it's passing the left MOSFET's current now.
When you turn off the +20V, VGS left is -10V and it turns off. VGS on the right is 0V, so it also turns off.
The diodes don't really figure into this circuit because both MOSFETs are either on or off at the same time, and the diodes block each other's current flow when the MOSFETs are off.