I am not quite sure what you mean by the timely process, but for every event one Party or other has to notify the fact that something is a compensation event. If the Contractor is notifying then they have to wait for agreement from the PM that they agree it is one, and then a request from the PM to provide a quotation.
There is no situation where the Contractor just provides a quote without being instructed to provide one. The only single exception to this is if the Contractor sates it is a CE, the PM fails to respond within one week, the Contractor reminds the PM he has not responded which the PM fails to respond within two further weeks. In this instance it is deemed accepted it is a CE and the Contractor should go ahead and produce the quotation. In every other situation the PM has to instruct the quotation.