The contractor is wrong. The early warning system is a management tool to help both parties work together to identify and manage risks to costs, time and quality, whoever carries those cost risks. In the case of ECC Option C, those cost risks will be shared between the parties.
Clause 15 on early warnings is all about risks which could, in the future, cause problems, so it is looking forward, not backwards. If you genuinely think that the way the contractor is carrying out the works may cause a defect in the future, you should speak to the project manager and get the project manager to notify it as an early warning.
Contractually, you can only notify a defect once you are aware of it, that is once it has happened (clause 43.2). Neither the project manager or the contractor can give an early warning of something that has happened.
For all these reasons the contractor is wrong to say an early warning must be given by the project manager before you instruct a search for or notify a defect. The contract simply does not say that.