Sorry I misunderstood. The term "read consistency" is generally used either in the context of isolation level or in the context of slaves.
We don't have standby instance, as I have mentioned we are using just one instance of postgres serving local clients running on the same machine, do you know in this case what is the behavior ?
You are good. All transactions update buffer cache too, along with WAL buffer and hence other sessions can immediately see the changes. synchronous_commit=off will only reduce the fsync calls, which makes them less crash safe, but the database consistency is not compromised.