I would think that watering deeply immediately after installation is probably not a good idea. You run the risk of rotting any roots which may have been damaged during handling. This may not matter very much if the roots did not break much, but there is certainly no rush to water at that juncture, and waiting a week is not any problem whatsoever for the plant. It would be waiting about that long in the nursery, most likely. Anyway, what's done is done, but I would think waiting 2 weeks to water again would be prudent.
Your aloe should respond well to regular water. It's drought tolerant, too, and will simply slow down during times of drought. But if your goal is a large tree, you'll benefit from giving it some attention during our dry summers. You're in San Diego, right?
My approach to watering aloes is more about frequency than quantity. Watering a tree deeply is a good idea, for sure. But the limiting thing is how long the plant may sit with dry soil in between watering. So I might water 5 gallons at a time, on a weekly basis. That's a good rule of thumb for the San Diego area during drought season, given soil that drains reasonably well. When the winter rains resume, you can take a vacation from watering. After a year or so of regular water, you can cut back as far as you like, to every 2 or 4 weeks maybe, and after a couple of years you could stop watering completely (though the plant would definitely slow way down during the summer as a result).
Skip the fertilizer for at least a year or two. I have never fertilized any of my landscape aloes, including trees, for going on 10 years now and they seem to grow and flower just fine. I mix some fresh compost into the hole when I plant (our soil is extremely sandy and rocky) and that seems to last a good while. You might try a light layer of organic mulch instead.