No person shall be relieved from liability for any income tax levied by any State, or by any duly constituted taxing authority therein, having jurisdiction to levy such a tax, by reason of his residing within a Federal area or receiving income from transactions occurring or services performed in such area; and such State or taxing authority shall have full jurisdiction and power to levy and collect such tax in any Federal area within such State to the same extent and with the same effect as though such area was not a Federal area.

The provisions of subsection (a) shall be applicable only with respect to income or receipts received after December 31, 1940.