The check-in limit for the M, L or XL membership refers to the calendar month from the first to the last day of a month. If you start your membership on the 10th of a month you have the full visit limit available to from the tenth until the last day of the month. Your visit limits would then reset again on the 1st of the next calendar month.
The exception to this is the S membership. The general limit of four check ins in total per month always applies to your membership month.