How you achieve parallelism in Extended Eigensolver routines depends on which interface you use. Parallelism (via shared memory programming) is not explicitly implemented in Extended Eigensolver routines within one node: the inner linear systems are currently solved one after another.
Using the Extended Eigensolver RCI interfaces, you can achieve parallelism by providing a threaded inner system solver and a matrix-matrix multiplication routine. When using the RCI interfaces, you are responsible for activating the threaded capabilities of your BLAS and LAPACK libraries most likely using the shell variable OMP_NUM_THREADS.
Using the predefined Extended Eigensolver interfaces, parallelism can be implicitly obtained within the shared memory version of BLAS, LAPACK or Intel MKL PARDISO. The shell variable MKL_NUM_THREADS can be used for automatically setting the number of threads (cores) for BLAS, LAPACK, and Intel MKL PARDISO.