Your organizations would open an account with one of these payment processors (if you don't have one already) and then authorize Auctria to process charges through your payment processing account.
The transactions are happening between your organization and your bidders and Auctria is just facilitating them.
Auctria And Stripe
Stripe is a tier-1 payment processor that handles all functions for secure transmission and storage of credit card information. Though the credit card information is entered in Auctria, no credit card payments or funds are processed by Auctria. All credit card payment processing flows through your Stripe account.
If you don't already have a Stripe account, it only takes a few minutes to complete the sign-up process online at stripe.com. To fully establish a link with Stripe, you'll need to input your bank account information to allocate where to deposit the funds. After completing the Stripe setup, you will be able to connect Auctria to your Stripe account so that you can process credit card payments for your Auctria auction charges through your Stripe account.
Stripe handles all credit card payment funds. Auctria is not a part of the financial transaction with your bank. After settlement and transit time (about 2-5 business days after the payment date) Stripe will transfer the funds to your bank account, minus credit card processing fees. See Credit Card Costs for more details on the fees involved.
Auctria And Authorize.Net
An Authorize.Net account can be set up as a gateway to a wide variety of existing merchant accounts. If you have an existing merchant account you can ask them if they support Authorize.Net. Be aware that there are fees associated a gateway account like this.
When using Authorize.Net as a gateway account the charge is processed by your existing merchant account, so you would pay the fees that apply to those transactions (and we do not know what those fees are). See Credit Card Costs for more details.