We had an Albizia in the irrigated part of our hot Greek garden, and was getting drip irrigation every 2nd night in the dry months. It grew and flourished for about ten years. As plants establish I cut down on their water, and two years ago, following that policy, I turned off the Albizia's supply altogether. I reckoned that as the soil in that part of the garden was good and deep it would be able to survive. However, though thoroughly established it is not really able to cope without irrigation. In the first water-less year it lost some branches, and after last year's very hot dry summer it died back much more, looking very pitiful.
So at least in our hot Greek conditions Albizias definitely need summer watering, even when established in a good depth of soil.