I'm not sure using examples of what was then acceptable discipline used in the context of a loving family is very useful to the OP, given the differences in his families set up, and the fact this is a new partner doing the 'discipline'
NP probably wants to contact you to minimise what she has done, probably like the above examples.
OP, it is not normal behaviour by any means, that a new partner waltzes in and does this to a child for discipline. Be warned for it escalating. If she is happy to do this at the start of a relationship with your ex, what's she going to be like when she has her feet under the table and relaxes.
I would definately inform his school, so they are aware what's going on, and if he does disclose it to them anyway, you are not left looking bad if he says, 'well mummy and daddy both knew'. I'd also seriously think of contacting social services with the information, you never know she may have had form for this sort of thing before, and that it's logged what she did to your son.
I would not have any contact with NP unless it's written down in black and white, email etc. reason being, if there are further instances, you have stuff written down, and also it's clearer to think and put down what you really mean to say especially if your feeling get up.