I have some experience with this. It's an ongoing saga.
I tried turning off chargeable SMS using ATM request mode but that never succeeded and ATM always showed some error.
Then called phone banking, the guy said he is turning off the alerts, but was still charged. Called again, same story.
Visited branch, filled up the paper form which has option to turn off alerts. Took a photo of the form, then gave to branch person, then he affixed bank stamp on it. I asked for it back again, took a photo with the bank stamp on the form, then gave it back to him. Was still charged. Waited for next charge, which also happened.
Emailed PNO, attached my photo of form, complained, mentioned RBI BO etc. Branch person called me, said he is again placing request, may be some problem with previous request. I said okay, and was issued some refund of charges. Also received SR number and notification that it was processed etc.
I thought problem solved, but no. Was charged again.
Emailed PNO, "I will be forced to complain to RBI" etc. etc. Branch guy called again. I said we have already spoken last time, what is your bank doing. There is no need to call me, just make sure I am never charged again etc. Received SR number again. Got some charges refunded. Also received email saying "as a one time service gesture we are refunding charges". I got irritated at this wording and replied saying "You are simply reversing these erroneous charges which were imposed because of a mistake on your side. There is no question of a "service gesture" here. The fact that I have to be on the lookout for these bogus charges and then follow up to get them reversed is in itself an indicator of the inferior quality of service provided by your bank."
I wanted to get this in the email chain as I have a feeling RBI Banking Ombudsman will have to get involved and I am going to demand compensation if I am charged again.
Received another refund of SMS charges from the bank.
Now let's see if I am charged again.
Moral of the story is Axis will keep charging and you have to push hard and you have to keep collecting evidence to present to the RBI Ombudsman. Do not accept anything over the phone, get everything in writing.