I googled: apparently there are two main methods used as far as when strikes take place, and other methods possible. The Judge has wide latitude in deciding which to use, but there have been sustained appeals for some methods.
For instance, one way not used in this case I saw described was to have both the defense and prosecution "secretly" write down their choice, strike or not strike. Then it's reviewed and if a strike is used by both, they both lose a strike.
There's no single set way, but I am sure HHJP is very aware of the ones that can cause an appeal issue.
I was surprised that the last juror was not stricken for cause and the defense had to use up a strike, but I'm happy about it