I'm completely baffled as to why you dug out the soil you had and have put in a mixture that is going to be very difficult to keep watered. What did you do with the soil that was removed?
Your soil mixture may also blow, but winds may not be a issue where you are. Speaking of that you're zone 8a but where?

I'm also baffled by the dirt replacement.

1 - Yes, you will have a "bathtub" effect, but it's less of an issue for vegetables.

2 - You will have a lot of settling as the tilled area compacts itself and the compost decays. Expect to spend the next couple of years topping up the garden with the dirt you paid to have removed.

2 - You need to mulch heavily with something (shredded tree branches would be nice) to retain moisture, and apply water more slowly.

From your description, it's created a channel down through the bed and just runs straight through. The fix for that is NOT more tilling, it's raking and rolling the garden to close up the channels.

I agree with lazygardens, you need to compact your "soil".
Also, don't water the area by running a stream of water from a hose. You need to water gently over a large area, one of those simple perforated metal sprinklers would do the trick.
Another thing, by creating this sunken bed or "bathtub" you may eventually have a salt buildup. With it being lower than the surrounding area runoff will naturally accumulate. This runoff may carry dissolved salts or other chemicals and there's a good chance it'll be left behind in your veggie garden. The runoff might wash out your garden too, you may need to divert it.
Of course a lot of this depends on your location in zone 8.

Thanks for the responses. I live in the high desert in very southern AZ.

I removed the original dirt bc I have heard over and over that it is the cause for failure of vegetable gardens in this area. The dirt is almost entirely clay. sounds like I should have figured how to work with it instead of replace it? I thought it would be beneficial to remove the caliche and with it came most of the clay as well.

The garden is now taking water quite well in the under layers, but it still easily pools on the surface. Underneath, I seem to get good moisture retention for many days. I think will be good for the plants when they are more mature. It's been a bit more difficult with the young ones...and seeds...to keep the surface damp for germination and initial establishment of transplants. I need a mulch, but have not found a good source yet.

I'm fearful of when the monsoons come...I'm sure my garden will flood out. I suspect I should plan to trench and direct the surface excess to run off instead of pooling...but I would like to have some of that rain soak in deeply as well. I have not thought about how to create that balance of keeping enough to saturate down several feet, but allowing excess to run off...any ideas?

Mulch will help. Clean grass clippings, old leaves, hay (watch for weeds but they'll be easy to control), straw (weeds again but not bad) are all good and often cheap. With the large amount of Afghan pines planted in my area, I watch for bags of pine needles set out on trash day. Our recent below 0 weather means I'll have a lot of free mulch this year. Pine straw is a great mulch but be careful in fire prone areas.
Layers of old newspaper make a good mulch but you do need to keep it from blowing. For transplants, lay out a nice layer of newspaper, cut large slits in it and tuck in your plants. I use about 5 sheets of paper for a layer and add to it as needed through the season. Too thin of a layer doesn't work, too thick keeps out any moisture yet holds too much at the soil level.
You can use regular pine bark landscape mulch. I like the big pieces, they don't blow or wash as easily as the fine stuff.
How far south in AZ are you? I'm in southern NM just above the border.
Re: monsoon
Catch as much of it as you can!
Rain barrels, buckets, trash cans w/lids, ...