The cable you purchased will not work. You need one the 1.8v version (TTL-232RG-VREG1V8-WE), but I’d recommend http://www.96boards.org/products/mezzanine/uarts/ instead and just connecting to it using a regular USB/microUSB cable. It’s a lot cheaper. Just plug the adapter into the LS expansion slot with the connector socket facing out and like you said, you will be able to have console on the default UART3 port.
I see from the OP-TEE github post that you already got things working. What else are you trying to setup? UART0 is also available but cannot be used with the adapter, so you’ll need the TTL cable above this time and also do some soldering to hook up to the board. See UART section in https://www.96boards.org/wp-content/uploads/2015/02/HiKey_User_Guide_Rev0.2.pdf.
You’ll also need to rebuild the software to use it: https://github.com/96boards/documentation/wiki/HiKeyUEFI#how-to-use-uart0-as-console