I am not referring to IPA. I am referring to examples in textbooks. For example, my Ukrainian textbook says that the letter Я is pronounced as "ja". Most native English speakers would pronounced this as it sounds in "jar", whereas the true pronunciation is closer to "ya" in my experience. This is a case where English speakers are explicitly the target audience.
This answer says that J has always had the same sound, so it can't be because of a change in sound overtime after the establishment of a convention.