Machine coordinates should be off when zeroing the Z axis.
The only way to zero the Machine Coordinates is to Ref All Home. This is typically done when first starting the machine, and provides a reference position for things like Softlimits, and tool change positions.
When you zero the Z axis, you are setting a Z axis offset relative to the machine coordinates. Once you zero the Z axis, you don't want to change the Machine Coordinates, as they will then change your Z zero.