I am not sure if I understand the in and outs of the question, but it seems to be that the PM is not accepting your notification of a compensation event on the basis that it does not fulfil the criteria in clause 60.1 (6) i.e. he/ she has 3 weeks to respond as per the Contract Data. From what you say, I am not sure if that quite matches the circumstances described in any case.
However, you are saying that you notified as a compensation event under clause 60.1 (3) as the PM accepted the programme with this date on it.
As a Contractor, you only have to find one heading listed as a compensation event for it to be a compensation event. So, assuming the "Project Manager's engineer" can be considered part of the Employer, then the PM is wrong to not accept your notification.
Even if the engineer cannot be considered part of the Employer, but an 'Other', then it could be a compensation event under 60.1 (5).
For it not to be a compensation event at all, the "Project Manager's engineer" / "engineer" would have to be either the PM, the Supervisor or a delegated sufficient powers to be considered such and what is 'sufficient' is another argument.