What you want is to force transactions to commit (making their inserts visible) in the same order that they did the inserts. As far as other clients are concerned the inserts haven't happened until they're committed, since they might roll back and vanish.
This is true even if you don't wrap the inserts in an explicit begin
/ commit
. Transaction commit, even if done implicitly, still doesn't necessarily run in the same order that the row its self was inserted. It's subject to operating system CPU scheduler ordering decisions, etc.
Even if PostgreSQL supported dirty reads this would still be true. Just because you start three inserts in a given order doesn't mean they'll finish in that order.
There is no easy or reliable way to do what you seem to want that will preserve concurrency. You'll need to do your inserts in order on a single worker - or use table locking as Tometzky suggests, which has basically the same effect since only one of your insert threads can be doing anything at any given time.
You can use advisory locking, but the effect is the same.
Using a timestamp won't help, since you don't know if for any two timestamps there's a row with a timestamp between the two that hasn't yet been committed.
You can't rely on an identity column where you read rows only up to the first "gap" because gaps are normal in system-generated columns due to rollbacks.
I think you should step back and look at why you have this requirement and, given this requirement, why you're using individual concurrent inserts.
Maybe you'll be better off doing small-block batched inserts from a single session?