I think the only test that uses those is the 16 types personality test and that is probably one of the most unreliable tests that I've found so far (except for ISFJs for some reason?). I'm pretty sure most of the community would agree with that, so usually when someone uses assertive or turbulent, people tend to become very skeptical of their typing.
The really don't correspond to much, maybe the Limbic vs calm in the global 5 test, but they are pretty useless when it actually comes to typing people
I personally think turbulent vs assertive are good indicators for someone’s personality sub type. There’s definitely a difference between an assertive INFP and a turbulent INFP, for example. It can make such a difference in how others perceive you, so I do wonder why it doesn’t seem to be discussed more in these forums. Using the same example, I could describe INFP-T as worry more about doing something to make others upset, feel envious often, just generally a more neurotic type. Whereas INFP-A would be more mellow about their decisions, don’t worry as much and overall more confident. These differences do matter a lot, IMO.