Testing whether a tetrahedron lies inside a Polyhedron
I recently found one solution to this problem in a paper 'Robust inside-outside segmentation using generalized winding numbers' by Alec Jacobson et.al., here. It solves the problem of locating if a point is inside(or outside) an arbitrary(one with self-intersections, non-manifold, open-surfaces etc.) polygonal mesh using the notion of generalized winding number.

Problem can be solved if I compute the generalized winding number of the centroid of $t$ against the surface of $p$.