Hokusai and Bernice Mai timing
The timing structure for accessing the server is:


  4 The Runner APPROACHES the attacked server.
  
  
    4.1 [Paid abilities]
    
    4.2 The Runner decides whether to continue the run.
        ...Either the Runner JACKS OUT: [end the run unsuccessfully]
        ...Or the Runner continues the run: go to 4.3.
    
    4.3 [Paid abilities and non-ice can be rezzed]
    
    4.4 The run is considered to be successful. (‘When successful’ conditionals meet their trigger conditions)
    
    4.5 Access cards, then [end the run].
  


Effects triggered by a successful run fire in 4.4. There is an opportunity to rez upgrades (4.3) before this step and after the Runner has committed to accessing (4.2).

To answer your final question directly, when I play, I normally say: "Would you like to access?", then, if they confirm, I say "Before you do, I rez...". (I actually ask if the Runner would like to access regardless of what's in the server.)