Only thing I know about turmeric is that it enjoys a hot, humid environment and very light soil. Are all of these present where you're currently trying to grow it? Perhaps a gentle misting with the garden sprayer in the area of where you have it planted might duplicate the humid condition it needs and check your soil ...is it light enough in texture?

Turmeric seems to just sit & do nothing & then suddenly sprouts at the right temperature. It will form little roots before it spouts. When it does sprout, it will grow rapidly.
I have no special growing instructions for turmeric, but mine are sprouting. Get a plump root, plant it, water it, be patient, & it will grow. I have dry heat, & put mine in the shade.