Have you actually tried using the controller while the lights are flashing? This sounds a lot like my experience on my MBP 15 (late 2013 model with video card) and PS3 Dualshock 3 controller (have not tried an original Sixaxis controller):
1) Connected via USB and held PS button down on the controller for a few seconds
2) Pulled cord out of PS3 controller then checked bluetooth settings - shows as connected but the lights were all off on the controller
3) Tested in a game on Steam at this point, Rogue Legacy. Controller functioned normal even though lights were off.
4) Closed game, told bluetooth settings to disconnect PS3 controller.
5) Turned PS3 controller back on, showed up right away in bluetooth settings as connected but this time all 4 lights on controller flashed fast.
6) Tested in game again and works normal while all lights are flashing.
7) Closed game, told bluetooth settings to disconnect PS3 controller. Lights stop flashing and controller shows as disconnected.
8) All subsequent tests have the PS3 controller flashing all 4 lights fast but working normally. I only looked this up to see if there was a way to make the lights stop flashing.