The data Mollie receives is processed under our own responsibility. Therefore Mollie is not considered a processor, but a controller as mentioned in the GDPR. This point of view is also explained in our Privacy Statement under 9, which you can read here.
This means that you are responsible for the safe and correct processing of the personal data you receive and you have to draft your own Privacy Statement. Therefore it’s not necessary to enter into a data processing agreement with Mollie.