The stadium in Tampa bay is a dome genius. The ball will change direction depending on the spin of the ball off the bat, just like a slider breaks depending on the spin the pitcher gives it. A lot more going on than just gravity.
Master Blaster makes a great point also, I guess not many people here have played baseball, we know Adonis was too busy with his ballet classes.
The direction of the ball off the bat is decided on how 'deep' the ball is. If a right handed batter hits a ball to left, he swung early enough to get his bat head in front. If a right handed batter hits a ball to right field he swung later and let the ball come closer to the plate.
The spin of the ball will only have an effect after it has traveled some distance, which is minimal anyways. Maybe I shouldn't have used the word gravity but a ball just doesnt change directions like that did. Your reference to a slider is a bit off, but thats another discussion.
maybe this helps.