[Kevin Sevcik]

So, what you were supposed to do is connect the servo directly (or through an extension) to one of the ports on the Futaba RC. You shouldn't have connected it to the Sabertooth. Read on to see why.

I'm going to start with a (brief) story so you know that I've been there too, then tell you what you did wrong.

Back when I was in high school on a BEST team, we built a small bot with a small arm we wanted to power using servos. To make the mechanical design cleaner, we mounted the servos back to back. Because this was BEST, we wanted to drive both servos with one channel, so we had to figure out how to reverse one of the servos. And I said "It's a motor, we'll just swap the red and the black wires and it'll go backwards!". (Al Skierkiewicz is shaking his head right now if he's reading this. Hi Al!) It didn't work and I ruined a servo and we had to mechanically change the robot and it was a terrible idea anyways.

I was completely wrong and ruined a servo for the same reason your wiring was wrong and smoked: Servos are not motors. There are a fair amount of fancy electronics in there including a potentiometer, motor controller, and feedback controller. The red and black wires provide power to the internal electronics and motor controller. That internal electronics is what powers the servo's actual motor. The white wire carries the signal R/C style signal that tells the servo what position to be in.

When I swapped red and black, it was like swapping red and black on the input power to your Sabertooth. It's a bad thing and ruined something inside the servo. When you connected red and black to the 12V output of your Sabertooth, it was similar to connecting the power input of your Sabertooth to, say, the 120V coming out of a wall socket. Too many volts not doing what's expected. Thus the smoke. I will tell you that even if you connected the Sabertooth to 6V and the servo hadn't smoked, it wouldn't do what you wanted. Changing the voltage on the red and black servo wires doesn't command the servo to move, changing the signal on the white wire does. And once you told the servo to go in reverse, it'd be just like my mistake and would've fried anyways.

Thus you should connect the servo to the Futaba, which provides the correct control signal on the white wire, and should provide the correct power on the red and black wires. I have no idea if your servo is still good, but I'd guess it's not. So find a new one and connect it that way.

TLDR; Servos aren't dumb motors. They're smart motors and their smarts can and will be fried if you connect their power (red/black) to too high a voltage or the wrong polarity. Plus the red/black wires don't control what the servo does anyways.