Yes, you need to do angle function calculation to get the tool radius offset if there is a combined XY probing.
Yes, the controller has to tell you the movement direction when the touch happened if the movement is an arc so then you can calculate the offset using angle function or the controller has to do the calculation for you.
I also see some complications about probing parts like on the video is that you need to know the part shape approximately to do the probing with somekind of strategy.