The TTL-232R-3V3 cable is wired for 3V3 signal levels, but it brings out 5V on the VCC line. To use this with a Pro-Min-3V3, you should connect VCC (from the cable) to the RAW input on the Pro-Mini-3V3. Power will then pass through the Pro-Mini regulator and supply the required 3V3.
If you connect VCC from FTDI to VCC on the Pro Mini, you run the risk of damaging the FTDI chip embedded in the cable. Your Pro-Mini should not suffer from this, but you may harm peripheral devices attached to the Pro-Mini that expect 3V3 logic and power.