When adding budget details for a new app, you will see that the budget type is set as Soft.
This means that the payment for that subscription will go through regardless of whether it is within the budget or it exceeds it.
There needs to be enough Available balance for the payment to take place.
Soft budgets are great for critical subscriptions, because who would want their website to go down just because Amazon Web Services charges them $20 more than expected?
If for some reason for one billing cycle you are charged twice the amount you have forecasted, the payment will still go through as long as you have sufficient available credit.
Don't worry, you will receive a notification letting you know about the payments that exceed your set budget, so no irregularity will escape you.