I had no idea what you were talking about so I looked it up.
Tamarind is:
"The fruit pulp is edible and popular. It is used as a spice in both Asian and Latin American cuisines, and is also an important ingredient in Worcestershire sauce, HP sauce and the Jamaican-produced Pickapeppa sauce."
I know when I was standing at a counter in one of the parks, waiting to pick up our counter service meals, someone asked a question about an ingredient in a item and the CM pulled a big notebook out from under the counter. In it was every item they served and all the ingredient and nutritional information about every item.
I would think that if you called Disney and asked them to connect you to the Tusker House that they could answer your your questions. As a courtesy, I would not call during real busy meal times.
I did find it listed as an ingredient at Jiko's at the AKL and at Anandapur Yak and Yeti Restaurant in AK.