I have solved the problem this way.
Please note that every test runs using a specific port of the iProxy, and the server of Appium works using another port. Both ports are defined through the following command line:
appium -p [appium port number] --webdriveragent-port [iProxy port number]
Two different tests cannot run using the same iProxy port simultaneously, and one of the two tests need to run using a different port from the one used by the other test.