In the case of a monthly reload period, you can choose to assign a pro-rata starting amount to the user.
For example: your user is entitled to €100 budget per month, but person X only starts on the 15th of the month.
In that case, uncheck 'Start amount = periodic amount'. Then enter the pro-rata amount at starting amount (in this example €50)
The user in question will only have €50 available for this (half) month and €100 for the following months.