I found this behavior while using the Col Cumulative Sum() as a way to create a counter.
If the group column has a missing value in the first row, the groups are completely ignored, see the last column below.
I replicated you findings. There also seems to be a relationship between missing values and the starting value of zero. Put a valid, but non zero value in row one and different results are shown.
Please turn your findings into the JMP Support team
support@jmp.com
Thanks so much for reporting this - we have replicated the issue in the Development team and it is on track to be addressed in a future version of JMP.