As Validators agree on the latest transaction sets to apply to the ledger when do they know to update the data being stored in the archive nodes?
Is it based on the owner of an archive node listening for quorum from a validating node that it trusts and then updating the history as each transaction set is applied to the latest ledger?
An archiver node (https://www.stellar.org/developers/stellar-core/software/admin.html#archiver-nodes) is a special kind of node:
when it sees a quorum (based on other basic/full validators on the network), it publishes to an archive.
Publishing is done every 64 ledgers if it's in sync with the network. You can read more about this in the history documentation (https://github.com/stellar/stellar-core/blob/master/docs/history.md#checkpointing)
