Dropping log on cylinder, proportions go out of wack

So I am creating a writing pen with a logo on it as a proof.  On the barrel of the pen is just a cylinder object stretched to the size I need.  I drop an AI file of the logo onto it and it sticks but the dimensions of that logo do not hold, its incredibly thin.  I can stretch it out in crazy ways just to make it look halfway normal but I feel like this shouldnt be necessasry.  Is there a step Im missing?