During the infect cities step, if an outbreak occurs and causes a chain reaction, then another city card is pulled which was involed in the chain reaction, does the chain reaction occur a second time? This can bump the outbreak track up very quickly (i.e. 0-8 in a turn).
The cards you draw to infect cities are independant from one another. Let's say the infection rate is 2. You first flip one card, infect the corresponding city (eventually managing outbreaks) then you flip the second one and follow the same process. If the second city is close to the first one and in the same color, odds are that cities that got an outbreak due to the first card will get another one... Nasty indeed...
The limit is one outbreak per city per chain reaction, not an outbreak per city per Infection phase...
From the Rules (Classic Pandemic p.7):
Draw cards from the Infection Draw Pile equal to the current Infection Rate and add one cube to the pictured cities, using a cube of the same color as each card. Resolve the cards in the order you draw them. If, however, the pictured city is of a color that has been eradicated, do not add a cube. If a city already has 3 cubes in it of the color being added, instead of adding a cube to the city, an outbreak occurs in that color.
If any of these new cubes would cause the total number of cubes of that color in an adjacent city to exceed 3, additional outbreaks may occur, causing a chain reaction. Note that each city may only outbreak once in each chain reaction