There are a lot of glicthes. As the other users had said, a motor "backfires" a lot of "hazard" / disturbs to the very power lines that feeds it. This is the reason why is not adviseable that you power your motor with the same power lines that you will feed your RPi.

But, which kind of motor are you using? Is it a servo motor? Is it a common DC motor (as in this second photo)? Is it a brushless DC motor? Is is a stepper motor? Every kind of motor has different requirements.

In this new form of the question, the yellow cube would be a circuit that takes 12V from the wall-wart, convert it to 5V, has protections from the motor electric noises, and sends this 5V to the RPi. The 12V from the wall-wart also connects to the controller of the motor.

A normal DC motor like this in the photo doesn't have three wires. That kind of motor has only two wires. So, the power from the wall-wart goes to the controller of the motor; this controller receives a digital signal from RPi, and when this digital signal is on, the controller sends power to the motor.

But at first you wrote "servo motor" in the question; after that, you put the photo of a DC motor; and recently the the photo in the question was changed again to a new kind of motor.

The L293 chip can control a motor, but it is not reputed as a very efficient one.

The IC or the module that will be used depends on the nature of the motor.

Do you already have the physical fixtures, i.e., the parts that, controlled by the motor, will release the food? In my opinion, that should be the first part of the project. Only if you have the motor attached to the physical parts that will release the food to some kind of tray were the dog will eat, is that you should start to think about how to control this motor.

You said that "I just need to spin the motor, one direction, for about a second. It is for an automatic food dispenser, so just a burst for a second or so, and I don't know exactly what type of motor I need for that. "

First you make your fixture and decide about the motor. Only after this you take the next step for the electronics control.

As an IT professional, you know that computers can't change things in the physical world by themselves. So, first, build the fixture to change physical things (the actuators or whatever else that will send a portion of food to the dog), and, second, think about the ways of put "brains" in it.