I think the two processes are being slightly confused here.
If either Party thinks their COULD be an issue that might affect time/cost/quality then they should notify an early warning and then have a meeting to see what if anything can/should be done.
If the Contractor becomes aware of an issue that HAS/IS going to affect time/cost and is not their liability then they can notify a compensation event, and if the PM agrees it is one they should request a quotation from the Contractor. At the point of requesting the quote, the PM could state 1) if they believe an early warning should have been given but hadn’t, and 2) state any PM assumptions that the quote should be based upon.
Stating no early warning means that the PM can take that into account if they believe the early warning would have meant they could have mitigated part or all of the cost of the compensation event. Stating any assumptions will mean the Contractor is clearer what risk they should or should not be pricing. These assumptions are the only elements of a compensation event that can be revisited after the quotation is implemented. Without such assumptions the Contractor would just have to price the risk that they can reasonably foresee.