Does this deferment apply to private school teachers or ...?

YES, distributed.

According to Article 23 of the Law of Ukraine "On Mobilization Training and Mobilization", during the special period scientific and scientific-pedagogical employees of institutions of higher and professional pre-higher education, scientific institutions and organizations who have an academic title and/or scientific degree, and teaching staff of institutions of professional (vocational and technical) education, institutions of general secondary education, provided that they work, respectively, in institutions of higher or professional pre-higher education, scientific institutions and organizations, institutions of professional (vocational and technical) or general secondary education at the main place of work by at least 0.75 rates.