A a service person, I am sure that you budget a certain amount of time per job. As long as the customers actions and questions aren't taking up too much extra time (maybe 5 to 10 minutes here and there) then I think that there is nothing wrong with the customers actions.
Customers fire companies all the time for doing things that offend them. What gets forgotten is that many times companies need to fire customers. A bad customer causes too many problems, and many times it is easier to cut ties rather than deal with a problem. Of course, this has to be done professionally, otherwise you risk bad yelp reviews,etc.
With that being said, if I were in your shoes, here is how my thought process would go.
Ask yourself these questions.
Do I have enough business that I can afford to lose this customer?
Do I have so much work that this customer is not worth it?
If you need (not just want but need) keep the customer, then I would ask the customer something like "When I'm here you are out here watching adn asking questions, which is fine. I like customers who are involved. But is there something that I'm not doing in a way that you like? I want to make sure that your needs are being met."
If they have no issues, and just want to learn more, you could move forward in the conversation with something like this. "I'm happy to offer some basic training for you, but unfortunately that takes a couple of hours to do properly, and that cant be done during my normal cleaning sessions. But we can schedule something, I usually charge $xxx for this service."
The reality of the situation comes down to this. If the customer doesn't want you to service their pool,it comes down to 1 of 2 things.
They are not happy with your work, and all you can do is find out what you can do better to keep them.
Or they want to do it themselves (either they are a DIY person or want to save money). For this situation, my sales sense says to stick around as long as you can, keep a good contact,and make money while you can. Remember that you do pool service to make money, and only paid for completed jobs. But if they are going to go DIY, and you can afford to lose them as a customer, the best way is to do it professionally and go ahead and help them transition to DIY as quickly as possible.
Of course that just my opinion, I could be wrong.