There have been similar compensation events some that the Contractor uses Subcontractor rates however on the latter ones they have used SSCC People rates included in the Contract, not all of the SSCC People rates align to those included in the 2nd quotation. I cannot see anything definitive what to use in this situation apart from SSCC.
The default position is that compensation events are assessed using Defined Cost - which will be by building up from the (Shorter) Schedule of Cost Components. The fact you have or haven’t been using “rates” previously seems to have been by agreement. Unless those rates are tied into the contract and intended to replace elements of the SSCC then they have no standing going forward. If Parties agree, rates or lump sums may be used, but this is on a case by case basis and no contractual precedent will have been set here no matter what has gone on before. I therefore agree with your last sentence.