The offer for a three month free trial is for new subscribers; users that haven’t had an (extended) free trial before. See the terms and conditions.
Read here how to redeem: Apple TV+ offer - Apple
Read here about the conditions: Apple TV+ offer - Terms and conditions - Apple
Read here if you have trouble redeeming: If you can't redeem your promotion for an Apple subscription - Apple Support
↳ Step 5 says to contact Apple if the prior steps didn’t bring a solution. They can assist.
… the salesperson redeemed the 3 months free subscription.
I don’t know what that means. The salesperson has no role in this. Only the first registered user of the new Apple device, if eligible, can redeem the offer. To redeem, the user has to click the “Enjoy 3 Months Free” button in the TV app, that should only appear for eligible Apple ID accounts.
I want to be sure I am not going to be charged double beginning in December.
No-one is charged double on the same account for any particular service. Users cannot have more instances of the same subscription on one account. If there are multiple accounts involved, then you can cancel subscriptions that you no longer want at any time. If you want to cancel a subscription from Apple - Apple Support