Tire size will certainly affect your overall gear ratio, a good general rule is that for every increase of tire dia. by 0.25", you should drop 2 teeth on your pinion. Depending on your final drive ratio and original tire size this could be different for your application, but it should be a good starting point. However, I dont think this is your issue since you say the car just takes off like you hit full throttle when you only give it partial throttle.

I would try to re-calibrate the system again, but make sure your radio settings are correct first. If you have a Futaba radio, or a Futaba OEM such as what comes with many RTRs, you will need to reverse the throttle channel before calibration. If you have EPA or ATL adjustments you will want to ensure they are maxed in both directions for the throttle channel, and make sure your trim setting for the throttle is at zero. Make sure you have good batteries in your controller and a fully charged pack in the car. If you still have the same trouble after re-calibrating it, you can try this: Re-calibrate again using slightly lower EPA or ATL settings, then max them after calibration. I am honestly unsure of why this has worked for some people, but I have heard of some calibration issues being corrected with this procedure.