Right now lots of foreigners hold USD for stability so the dollars aren't circulating.  Once the dollars come back to the US and begin to circulate, there will be tons of dollars chasing less and less goods and services.  That is why inflation will get so much worse.

Yes, the right get the new money first before it has deflated and yes other Americans get the money before it moves around the globe and therefore get a little of the benefit before it is fully deflated.  Still, so much is just being held in reserves that we haven't seen the full effect.