First of all, you need to see if what he told you is some very professional terms, because a fitness instructor needs to take professional fitness exams and have a certain understanding of various fitness standards, so if he is already discussing courses with you, he must know these professional things like the back of his hand, so you must express your doubts and see if he can explain them to you clearly.
Secondly, if you can, you can ask your coach to show you his coaching certificate, because these are all necessary documents for a coach. It's totally unrealistic to say that you don't even have a certificate to teach directly. If you find him refusing or hiding, you must cancel all the courses of this coach in time, because he is probably just a coach who does not have the quality of a professional fitness coach, which is very harmful to your next fitness.
Actually, you don't have to hire a fitness instructor. You can find a fitness method that suits you online. Every gym will have a private training experience class. You can choose this course as a way to get familiar with the equipment, let the coach teach you how to use all the equipment, and then you just need to practice according to the online recommendation. There is no need to spend a lot of money on a personal trainer.