Yes, the test utility that comes with USB-serial SDK for android cannot be used for testing UART functionality. It should be used only for I2C/SPI functionality.
Also, note that CY7C65213 can be used in either vendor mode or CDC mode. You need to compile the library only if you are using the device in vendor mode.
To verify the UART functionality in CDC mode, please go through the Knowledge Base article available in the link: http://www.cypress.com/knowledge-base-article/testing-usb-serial-bridge-controller-configured-usb-uart-android-kba92550
It is suggested to confirm whether the device is configured in Vendor mode or CDC mode using USB-serial configuration utility that comes with Windows SDK.
If you are still facing any trouble, I recommend you to create a technical support request at http://www.cypress.com/support