A vehicle's registered owner must request a smog exemption due to vehicle being out-of-state. Your name would be added as the "out-of-state vehicle operator". You may either have your spouse transfer the title to your name and then you request a smog exemption, or the simply method would be to have your spouse request the out-of-state exemption.
Please contact the DMV at (800) 777-0133 for further information. Typically the DMV requires 4-6 week for registration response, however we'd recommend calling them just to make sure your paperwork is in order. They may or may not have processed your request if the vehicle's registered owner information and signature did not appear on the smog exemption request form.