How do "Run" Events interact with effects that change the server you're running on?
As CrystalBlue commented, the latest copy of the FAQ (PDF) addresses this (page 2):


  “If successful...”
  
  Whenever there is an “If successful...” effect tied to the outcome 
  of a run, the run itself must have been successful against the 
  specified server(s), if applicable. If the Runner initiates a run 
  against the specified server but ends the run on a different 
  server, the “If successful...” effect does not resolve when the run 
  is successful.
  
  Example: The Runner plays Demolition Run on HQ. During the 
  run, a Bullfrog moves the Runner to a remote server. Even though 
  the run is successful, the Runner cannot use the “If successful...” 
  effect on Demolition Run because the run was not successful 
  against R&amp;D or HQ. If the Bullfrog moved the Runner to R&amp;D, 
  the ability would trigger when the run was successful.
  
  If the “If successful...” effect does not specify a server, then it 
  does not matter if the attacked server is changed during the run 
  ,and the ability resolves as normal.


In summary, if a run ability specifies a server (or servers), the "if successful" effect only triggers if the run is actually successful on one of those servers. As the example in the FAQ mentions, it does not need to necessarily be the actual server the run was initiated on though.

For Account Siphon and Maker's Eye, if the run does not finish on HQ and R&amp;D respectively, the special ability is wasted (and the run essentially just becomes a normal run).