just a thought: jog the z without a tool down as far as it was when you made that cut. Put an indicator off the table touching the nose. pull down on the head and see if you can get a thou or three of movement. These aren't insanely rigid machines. There is bow, flex and movement in the ball screws, gibs, base, and some thermal growth over time/temp. Add it all up and it can easily be 0.004" when indicating vs a 1" deep side cut. Your helix is pulling UP on the plate. Newtons law says it's pulling down on the head/ball screws/gibs as well. you likely lifted the table .001 and pulled the head down .002 and the spindle grew 0.001 = .004 (as an example). Even LIGHT cuts are not light cuts when there is a 1" DOC and a high helix EM pulling down on the head/up on the table. Just pointing out there are a million things that want to move. If you put the indicator on the head and touching the table and lift up on the table you will see 0.001+ movement. Mind you... I see movement when I do any of these on my Haas and Brother as well, less, but flex is ALWAYS there. Thermal growth is as well unless the entire machine is made of granite.
In the end there is a reason all controls usually have such easy offset adjustments... Program 0.005 HIGH and measure/inspect, adjust offset after seeing real world conditions applied to the cut and repeat the finish cut or program for a final finish cut. I do very tight tolerance work (+/-0.0005) all. day. every. day. There is only one way to hit those numbers and it's raking rough/finish/measure/finish again/measure/finish again. Even if I get it right at 8am it's wrong by 845 and needs the same process repeated over and over. 300+ parts a day and the same process on them all.