When do you increment the 'Successful run' counters?

Question

Do you increment your 'Successful run' counters at the moment you successfully went through the ice(s) and are accessing a server or do you increment your counters after a run is completed?

For example: With Medium virus (anarchs), incrementing during the run would affect the number of card you can access.

Medium: Whenever you make a successful run on R&D, place 1 virus counter on Medium. Each virus counter after the first on Medium allows you to access 1 additional card from R&D whenever you access cards from R&D.

Answer 1

Add tokens, then access. There's a timing structure in the FAQ (here). The end of the run goes like this:

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].

The run is considered successful (and tokens are added to Medium and the like) in 4.4. You access the cards in 4.5.

To answer the question within the question, this also means you'll get extra cards starting from your second Medium run, and not just starting from your third.

Answer 2

The run is considered successful BEFORE you access the corporation's cards. From the rulebook:

Access Phase
After the Runner has passed all of the ice protecting the attacked server, he has one final opportunity to jack out. If he chooses to continue, the Corporation has one final opportunity to rez cards. After rezzing cards, the run is considered to be successful and the Runner accesses the Corporation’s cards by looking at them.