Gravity takes effect,
Gravity is always in effect. It doesn't just kick in.
Now, since everything is moving at a very fast speed upwards, if you walked off a ledge, you'd be travelling at the same speed the earth is, and you would not fall, because there is no force pushing you down, and when your feet were on the ground, you were being accelerated with the earth.
Nice violation of the Newtonian laws of motion.
Let's take a look at how the three laws of motion really apply:
You are standing on a cliff. By the 3rd law, you push on the earth, the earth pushes on your feet. This means that as the earth accelerates, the force is applied to you. So at any instant, you are traveling at the same speed as the earth. Now, you jump off the cliff.
By the 3rd law, you are no longer have the force of earth on your feet, and by the 2nd law, force is now zero, so acceleration must also be zero.
By the first law, you will continue with the same velocity that you had when you stepped off the cliff. However, the earth is still accelerating, and has gained velocity since you left the cliff, so the ground rushes up to you, and then you die.