Yes, SPF (Singapore Police Force) expects you to send the invitation (with the names of the applicants being listed in the invitation) for them to issue the CoC.
If the invitation letter from CIC doesn't have your spouse name, you can still proceed to submit your profile without the Singapore PCC of your spouse. Just write an LOE explaining the same and requesting a new invitation with your souse name included. CIC then will send you a new/updated invitation in a month or so and gives you time to obtain the CoC.
My case a little similar. My spouse and I had lived in Singapore and so we needed to include CoC in our application. ITA sent by CIC has only my name, being the primary applicant and SPF rejected to issue CoC for my spouse as her name wasn't listed in the invitation. We prepared to proceed with the application without her CoC but just a trail, sent an explanation to SPF that CIC issues invitations only to the primary applicants and not to the dependents. To our surprise, SPF accepted that explanation and issued CoC to my spouse too. Now we are in process of finalizing other documentation to proceed with the submission.
It may or may not work for you but you can still try. Just write to SPF explaining the scenario and request to issue CoC. Make sure you provide enough evidence of your relation (primary applicant on CIC and the dependent seeking CoC from SPF). Still, be prepared to submit your application without dependent's CoC.
