The day you make any purchase for a recurring payment will be the future date of your regular payments.

For example…

If you are paying for your club membership on a monthly basis and you joined the club on the 6th of the month, then all your future payments will come out on the 6th of the month too.

If you are paying for your club membership on an annual basis (and have an annual book subscription) and you joined on the 6th of November 2018, then your next annual payment will come out on the 6th November 2019.