This occurs when milling on the outside, and the Chuck will loosed. For pockets the Chuck is tightened
solutions
1 obtain opposite helix mills. Difficult to find and expensive Reverse motor
2 use straight sided silver steel endmills like d bits. Reverse run
3 drill through backplate register and fit a decent sized grub screw Dimple into the Mount. Or, fit a pin
4 make up a fitting which is bolted to the table going under the backplate and pressing hard against the Chuck fixing bolt , or fit a hockey stick shaped one into a cavity in the back of the Chuck if there is one fir chucks without backplate
this is a problem on my big dividing head when set vertical. Solutions above not possible, so constant pressure needed on the Chuck key to resist any tendency to resist any movement
this is why the horizontal spindle on either dividing head or rotary table is best in this situation.
like you I look forward to seeing other people’s solutions!