Do $s$-$t$ cuts partition contingent vertices?
The example is correct: in this $s$-$t$ cut the capacity of the cut is indeed $3$. However, the min-cut in the max-flow min-cut theorem talks about the capacity of the minimum $s$-$t$ cut. So one must take an $s$-$t$ cut that gives minimum capacity: what you have in your example is not one of them.