The only way I know to make a teriyaki flavor at home is a combination of shoyu and honey, but honey is not vegan!  I think you'd have something similar using brown rice syrup and I have done that too, but the flavors seem more subtle.

I don't know what the tofu appetizer is, but I am thinking it might be agadashi.  For that, you need to dredge your tofu cubes in flour, then in plain soymilk and finally into panko crumbs and fry them.  You dip the cubes in ginger shoyu, which you can make or buy (make by taking shoyu and adding grated ginger).  Agadashi is crisp outside and creamy, buttery like inside.  I have made this for dinner, but using it as a starter is better because it is so good, dinner takes 4 lbs of tofu to feed my whole family of 4 growing girls.

Let us know what you found.