How does ATC handle changing QNH/altimeter values?
In the US, ATC simply broadcasts a notification on whatever frequency is needed. For the terminal environment, section 2-9-2 of the ATC orders says:


  Broadcast on all appropriate frequencies to advise aircraft of a
  change in the ATIS code/message.


The phraseology is usually something like this:


  Attention all aircraft, Bowman information Kilo is now current.


For en route operations (see section 2-7-2) the ARTCC gives altimeter setting updates directly:


  Attention all aircraft, the Nashville altimeter now 2992