Each machine doesn't have its own commit log at the level of the distributed database. (The key/value store where we locally store data on each node happens to also use write ahead logging, but this is not an architectural requirement). Ideally transactions just have to be made durable in some N places to be considered committed. In practice, we elect specific machines to a transaction logging role, among other reasons because SSDs do better at providing fast durable commits if they aren't also serving random reads.
Each machine is authoritative for reads for some ranges of the keyspace and for the range of versions it knows about. It proactively fetches writes for newer versions. If it gets a request for a version it hasn't managed to get the writes for yet, the read has to wait while that storage server catches up. In practice this lag is very small, as you can see from our latency measurements.
Specific questions: does each machine have its own commit log? Is each machine authoritative for its range of the keyspace, in that it can serve reads without having to consult other machines?