Using a digital signal to turn on and off a vibrating motor

While perusing the IOIO board link provided in the question, I noted that the board has some 5V tolerant open-drain digital output pins. Since the camera has built in pull-ups, as shown in the first diagram in the question, you should be able to connect the open drain pins directly to the camera. You will not even need the external transistors.

The current sink capability of the open-drain outputs is specifed at 20mA, which easily will handle the .5 mA mentioned in the question.

In this case, the camera "expose" and "focus" would be connected to open drain outputs, and the camera ground would be connected to the controller board ground.

edited to add:

I now note that the page you cited in the question, http://www.covingtoninnovations.com/dslr/CanonRelease.html, advises adding an optoisolator to the circuit if the camera will be powered by an AC adapter rather than the camera battery, as shown in the second diagram in the "Serial-Port Cable" section. That is probably a good idea. In that case, you could connect the optoisolator to an output pin on your controller board that is not an open drain pin, selecting a dropping resistor to set an appropriate drive current for the diode.

Your motor that you linked to is a 4.5V 190~250 mA (No Load) motor. At 9v, the current probably increases. You are overdriving it by 200%. And any load/weight will cause it to increase in current requirements as well. Stall current is probably 10x that at least.

You are missing the protection diode across the motor, that can easily kill the transistor.

The Transistor you are using is a 100mA standard, 200mA Absolute Maximum. One of those motors by itself without any load, can easily kill that transistor.

The base resistor is calculated as (Base Voltage - Base-Emmiter Voltage) / Current required. Base Voltage is the Arduino pin, so 5v, Vbe depends on the collector current which is 200 mA here, so typically 1V. Current required is calculated as Collector Current (200mA) / Hfe (From datasheet, 10~30). On the safe side, lets go with 10, so 200 / 10 = 20mA needed at the base.

(5V - 1V) / 20mA or 4V / 0.02A = 200Ω resistor. A 1kΩ resistor would only allow 4mA at the base, which times the Hfe of 10, would only allow 40mA at the collector, probably no where enough to tun on the motor.

TLDR: You need the protection diode, your 9v power source is too high, and your transistor is too weak for the motor you are using. And you need a bigger resistor at the base because the motor requires more current then you are figuring. A common 2n2222 transistor with a 470Ω resistor would do much better.

Edit: Not making the pin an output also puts a damper on things. Answer, Arduino pins default to input.