Usually the PM should state the date of Completion on the certificate which by clause 30.2 might be up to one week before he issues the certificate. The date the certificate was issued is irrelevant other than demonstrating that the PM did in fact issue it within the required time frame.
Note that possession as a concept isn’t used in NEC, so the Contractor never has possession and therefore the Employer never takes it back. The Contractor merely has access to the Site (clause 33).
Clause 35 deals with take over, in particular clause 35.1 requires the Employer to take over no later than two weeks after Completion. There is no need for the PM to issue a take over certificate unless the Employer has taken over any part of the works (clause 35.3).
Let’s say the PM decides Completion has occurred on the 1st Dec, he has up until the 8th Dec to issue a certificate that states this (clause 30.2) and the Employer must take over by 15th Dec (clause 35.1). The Contractor is liable for loss of or damage to the works, Plant and Materials until the Employer has taken over (clauses 80.1 and 81.1) and as such will need to provide whatever resources are needed to ensure this risk is mitigated e.g. site hoardings, security etc. So yes, potentially you should have allowed something in your tender for the period between Completion and take over but that’s a Contractor’s risk which you would no doubt take a commercial decision on how to price.