Acoustic registers are discussed at length by authors such as Coffin and Bozeman. They result from an interaction between the the resonances of the vowel and the pitch being sung along with its component overtones. To many, acoustic registers sound like colors of vowels, because essentially they are! This, I believe, is why some teachers and singers disregard the idea of acoustic registers, because they view them as features of the vowel. However, regardless of how they are viewed, the resonances of the vowel interact with the overtones of the voice and that is a reality that has to be reckoned with one way or another.
The vowel is created by the relationship and relative placement of the two lowest resonances of the vocal tract (called the 1st and 2nd formant). We adjust these resonances and thereby create the vowel by moving our tongue, lips, jaw, vellum, larynx, pharynx, etc. When the sound generated at the larynx, which naturally contains overtones, is filtered through the throat and mouth we get what is commonly referred to as "resonance." This resonance is basically the sound of the vowel. There are higher resonances of the vocal tract that are also important for the ring and resonance of the voice (the so called singer's formant), but these have less bearing on the acoustic registration of the voice.
When the first (and to a lesser degree, the second) formant change their interaction with the overtones of the voice - i.e. changing from one overtone to another or none at all - we experience some degree of acoustic register. This change can (and often does) occur whenever the pitch or vowel is changed. These registers are felt and heard the strongest when they result from interactions with the fundamental frequency (the pitch being sung) and the first overtone (one octave above the pitch being sung). These interactions are responsible for most of the passaggi traditionally discussed in vocal pedagogy, the distinction between voce chiusa and voce aperta, covered and open timbre, and a myriad of other terms.
Most great singers and teachers understand these relationships and changes intuitively and through the experience of years of listening and singing. However, it does not take a a lifetime to learn to hear and understand the experience of acoustic registers. The instruction of vocal pedagogy should focus on hearing the effects of acoustic registration and learning the tools at ones disposal for exploring resonance. Armed with this knowledge and auditory information, teachers of singing can guide their students to the proper registration and vowel choices through whatever methods they find most effective with that student. Without this understanding, registration, especially in voice types that are not ones own, can be a daunting and baffling concept for young teachers and a hindrance to their effectiveness with their students.