Yes, probably (I don't know the details in VASP, can only answer for ATK).
ATK uses libXC for the implementation of the functionals, and you can check the references there, although you sometimes have to "interpret" our keywords a bit. The OneparameterB88 corresponds to XC_GGA_C_OP_B88 with reference T Tsuneda, T Suzumura, and K Hirao, J. Chem. Phys. 110, 10664 (1999).
