Yes, it is possible to have credit card processing set up to apply the funds to different bank accounts based on which web site the order was placed on.
The transfer of funds to the bank account is the responsibility of your Payment Provider and Pressero only allows the user to get connected to your payment provider in order to make the payment.
In order to achieve your goal, you may have to take more than one account from your payment provider, each account will be linked to different bank account and then you can create different Payment methods
using these credentials and assign it to different sites.
This way based on the site that is getting the order the money will be allocated to the associated bank account by the Payment Provider.