exchange rate and domestic money supply part II
@Toby comments noted, I will attempt an answer.  First, the FX market is international so you cannot tell whether the foreign currency seller is domestic or foreign. However, if it is a foreign buyer, they will typically reinvest the dollars in either a commercial or financial asset such as a Treasury bond, which could result in the remittance of the dollars back to a domestic holder.   What you know for sure is that the dollars will be deposited in a bank somewhere and will add to the pile of excess reserves currently held by the US banking system.  Hence technically the money supply goes up.  

Perhaps the greater question is whether raising the money supply in this way has any effect on the economy.  I would suggest not, since banks already have excess reserves.   Rather, the transmission mechanism for FX intervention is via changes in the exchange rate.   But that could be debatable.