It turns out the website had the wrong relay datasheet so the pinout was wrong.
Anyway, I made a small circuit that turns on and off an led every 3 seconds with Arduino through the 2N2222, relay and the 12V 1A PSU and it worked great. I then replaced the led with the motor I'm using for the project but instead of turning, it moves like one tiny step each time the relay's coil is turned on.
The motor is supposed to work at the given current and voltage. For the led I did put a resistor but not for the motor.
Any idea why this is happening?
Thanks