The location of the thunderstorm cells and the route of flight were updated continuously after takeoff in order to continue avoiding the areas of bad weather. Approach Control was also able to vector or assist the aircraft in avoiding bad weather but the ultimate responsibility was the responsibility of the aircraft crew. The aircraft crew also maintained radio contact with their dispatcher who had access to numerous resources to continually update the crew and modify the flight route to maintain a route that best avoided thunderstorm activity.
Today the process is very similar however current generation aircraft have much better on board digital weather radars and flight navigation displays that allow the pilots to see how the weather affects their current route of flight. It gives them the “Birds Eye View” depiction. It also displays the winds and temperatures at altitude allowing the flight crew to continually monitor and adjust their flight plan and route of flight to provide the best ride available to the passenger.
Even though the thunderstorms can be avoided it is not always possible to avoid all the minor turbulence that is produced by the thunderstorms, jet stream winds aloft and other factors.