Binding properties of turmeric
Turmeric is a rhizome that contains some starches. Those starches will hydrate and gelatinize like any other starch and thicken liquid. 

I don't know how its thickening power compares to other starches like flour or corn starch. This paper has a chart of vegetable starch sources that would imply that turmeric's starch content is fairly high at 76%

In many cuisines turmeric is used for color and flavor and isn't present in enough quantity to have this effect. As you have observed in Indian curries enough is used to thicken a sauce.

I add turmeric early when frying all the other spices to toast them. As with other fine powders, frying it early also makes it a bit easier to incorporate without clumps.

The only reason I can think of to add it later is if you are adjusting the flavor/thickness of the curry.