How exactly do cures affect future infection in Pandemic?
Scenario 1: continue adding cubes, as you have been doing all the way along. The example of "Playing the Infector" specifically states: "Even though the Black disease is Cured, it can still spread!")

Scenario 2: nothing happens. The rules state:


  Eradicating a Disease
  
  If a cure for a given disease has been discovered and all of the disease cubes of that color have been removed from the board, flip the Cure Marker for the disease to the "Sunset" side. From now on, cards of this color have no effect when drawn on the Infector's turn (emphasis mine -- StasK). Take all of the cubes of the eradicated color and place them back in the box -- they will not be used again for the rest of the game.


So finding a cure affects the game via the change in how "Treat Disease" action is played.


The Medic character starts treating the disease without spending an action: if say the red vaccine has been discovered, whenever the Medic is in the city with these red cubes, he or she can take them out without spending an action. This also means that the Dispatcher (or the Airlift special event) can throw the Medic into a red city that is about to outbreak, and the city will be cured with no other actions spent by any of the players.
All other players can remove all of the cubes in one action (rather than just one cube) when they treat disease in a city.


In the longer term, discovering the cure makes you one step closer to the victory -- you need to discover all four cures to win the game. The Infection step, however, is not affected by the discovery per se -- only by eradication.