I don't think you have to worry about over watering a raised bed, especially if it can drain through the bottom or gaps between plants / stones / etc on the sides. In my garden I have several raised beds and several areas that I plant directly in the ground. My watering system allows me to water each bed individually as needed - sometimes I'll forget to turn the water off overnight or while I'm at work during the day in one of the beds - the raised beds are always fine, but in ground beds fill up with water. Until you get used to the 'right amount', water for a little while and then dig small hole and see how far down the water soaked into the soil. Eventually, you will get a feel for when your plants are thirsty. With a nice layer of mulch, it's much easier to keep the soil consistently moist.
