I've recently been removing stumps of large trees on my property with an excavator which has been informative regarding tree root growth on the site. Though I didn't dig up any mango trees I will take a picture later today of the exposed root system of a large mango tree on a neighbor's property which was overturned by hurricane Irma. I'm also digging an irrigation pipe trench across the property and observe some variation at least in the top 18".
My soil type is the most common in Florida, Myakka. The soil is gray sand topsoil which lightens to white sand about 18" down, then becomes very dark brown in a highly compact layer.
As seen in the video Cookie Monster referenced, mine is very close to what is shown here:
The change in soil color matches the summertime high water table, and also matches the maximum depth of root development I've seen in the stumps removed and in the overturned mango tree. This zone of compacted soil representing the high water table also represents the zone of oxygen deprivation below which few roots can exist regardless of what you do. I can track water table by nearby ponds which vary according to the water level.
This reference "Tree roots: Facts and Myths" shows a lot about how tree roots grow.
http://arnoldia.arboretum.harvard.edu/pdf/articles/1989-49-4-tree-roots-facts-and-fallacies.pdfI find it amazing how wide tree roots can go, how they graft together, how one root can feed one segment of canopy, how the microfauna infinitely extend the root zone, and all the other factors we don't even know about.
I know there are many other soil profiles around and yours may be quite different. Some have soil similar to mine. If you find a nearby excavation, find a tree root system exposed or even use a post hole digger you can get an idea of what you have. So, when to water really depends on your soil and the more you can learn & observe locally the better you will know what to do about it.