I often baffled on how some teachers take that phrase for granted. For starters I have no idea what it means. When a teacher says, "Be careful with your tails sounds." Does she mean that the student should pronounce the extra phoneme carefully? Or is it an euphemistic language saying and sublimely saying for the student not to say that anymore.
As an ESL teacher I find that confusing from the point of view of students. What are tail sounds? I never learning about tail sounds in English sounds. I know there are final sounds but never tail sounds.
What most Koreans are doing is what is called Konglish or more precise - Konglish pronunciation. We know for a fact that some English words have been adopted into to Korean language but somehow the word mutates into a Korean pronunciation. There are sounds that cannot be clearly adopted and had to be changed and thus the same thing also happens in Japanese.
Thus we have the following words:
오렌지 (orenji) for orange
테니스 (teniseu) for tennis
나이스 (naiseu) for nice
슈퍼마켓 (syupeomaket) for supermarket
You can see from this example that not all words have the so called tail sounds. Some of the added phonemes happen within the word itself.
So don't expect me to be careful with my tail sounds. Please!