I honestly doubt this is the case. If the gravity were stronger, they would receive a massive boost in strength on our planet, and only a small speed boost. Either way, it would in no way improve their reflexes and reaction time. Their body would be proportionally stronger on Earth, but their minds would be no different.
Also, in general, picture the motion of running. Each step is like a small leap, right? Well, if Earth's gravity was that much weaker than on planet Garatron, if they tried to run, those little leaps would turn into massive jumps and they wouldn't really get that far. Think about how human astronauts walk on the moon. Every step basically launches them in the air, and they don't really move that much faster.
Also, if the planet's gravity was that strong, how could the Yeerks establish a base on it? Any controlled species at the time would be immobile, unable to pick up anything, or in the worst case, crushed.
As far as I can think, there are two possible explanations. One is simple - speed was selected for in evolution for millions of years. If a predator gains speed, so will the prey. Two, the atmosphere is incredibly dense. Imagine running through water, then running on land. This also explains the Garatron's shape - aerodynamics would be greatly favored on a planet with such dense air. Maybe the Garatrons run only slightly faster than an Andalite on their own planet, but when put in a thin atmosphere with significantly less drag, they can run much faster.
Still, I think it's a simple fact that they evolved that way. No immediate physical or environmental change can explain why the Garatrons think and speak so fast. If they naturally run that quick, fast reaction time would be expected if there weren't to be running into things all day at that speed.