Yes. Client billing dates are set in the agreement.

If your client approved an agreement on May 30th, and the billing date is the 1st of every month, they'd get billed for May on June 1st.

If you would like to apply prorated billing for a service (the invoice for a service is calculated based on the cost per day or the proportion of the monthly service used) you can do so when setting up the service under the client agreement, as seen below: