The OLED uses SPI. The CS of the OLED does exist internally, but it is wired to GND (always active).
The U8GLib library will work with it, both the hardware SPI and software SPI. That library also has a CS, and I choose an unused pin of the Arduino for that.
I don't know if your OLED will work with Adafruit library. There might be a few differences.
I know that this is an older post, but I would like to hear if you managed to solve this problem - as I'm having similar issues with a display that looks just like yours (except that I actually got the CS pin).
The top 10 (or so) pixels works fine, but the rest is just rubbish .. and it makes no difference if I disconnect the CS pin - everything just continues as nothing happened. (wooot?)