I am told that transfers of $4,000 or less require no confirmation as to source of the funds by Banco Popular, and that is consistent with my experience. Funds arriving the next day if made by ACH wire.
Anything above $4,000 is held by Banco Popular for a few days until I contact them and confirm the source of the funds.
The $4,000 figure is, near as I can tell, an arbitrary sum pulled from the ether by BPO, and not a requirement imposed on the international banking system by the US government, like the requirement to report any transaction more than $10,000.