It appeared that Ideel doesn't allow to enter addresses outside the USA for both billing and shipping, so entering my complete real billing address in Russia was not an option. I tried to enter my real name, real street address and to use the rest from my Shipito virtual address, but it didn't work. Then I tried to use my US virtual address for both billing and shipping to no avail. Then instead of checking out I went to the account settings and tried to add my card from there. I was getting the same error no matter what address I was using.
It appeared that many customers from Russia and other countries have faced the same problem. This happens because Ideel verifies that the billing address provided matches the one on record with your bank. You need to contact Ideel support to disable this AVS system. Then you should be able to check out using a foreign credit or debit card.