The 300 minutes your inmate gets each month are controlled by the Bureau of Prisons, not by InmateAid. The BOP resets that allotment on the same date every month, but that reset date is specific to each inmate and is set by the BOP when the inmate first enters the system. It is not necessarily the first of the month. It could be any date depending on when that individual's account was established.
Once those 300 minutes are used up, your inmate will need to wait for their personal reset date before the allotment refreshes. There is no way to purchase additional BOP minutes on top of the monthly allotment. The 300 minutes is a hard cap set by federal policy, and it resets on schedule regardless of how quickly they were used.
What InmateAid controls is the phone line itself, which recharges every 30 days for five dollars. That renewal keeps the local number active so that when the BOP minutes reset, your inmate can continue calling at the lower local rate. The InmateAid charge and the BOP minute reset are two separate cycles that run independently of each other.
The practical takeaway is to pace the calls as the reset date approaches if minutes are running short. If you are not sure when your inmate's reset date falls, they can check that information through their phone account at the facility.