Thank you for your reply.
This environment will start counting time delay from the moment it receives spending transaction and will co-sign only when time delay has passed.
So if a user sets their CSV timelock to 15 days, that timer begins as soon as they send coins into the wallet and at this point key C cannot sign transactions because of the CSV timelock. But if more than 15 days pass, the CSV timelock expires and key C can sign. However, it sounds like key C will still not sign because key C is controlled by the CS which only begins counting down its time delay when it sees a transaction spending funds out of the vault.
If this is the case, why bother with the CSV timelock at all? I don’t believe I understand the purpose of the CSV timelock. Most users presumably would like to keep their coins in the vault for more than 15 days.