Typically with a forecast like this, the captain would opt to carry some holding fuel - this is in addition to the planned diversion fuel to a suitable alternate and the contingency and final reserve fuel all of which add a decent buffer. The flight crew will have had a look at the airports nearby to ascertain which airfields are likely to be storm free for the period around your expected approach and added fuel to be able to divert as necessary.
So you need to know that with few CB's it's not automatically implied that there are thunderstorms over the airfield - it's just possible that thunderstorms may occur from those clouds - and by looking at weather radar it's possible to see whether there are storms and areas of heavy turbulence in the area. The idea would be to fly towards the airport carrying all of this extra fuel, listen to the actual conditions reported by the airfield as you get closer and decide to try an approach if suitable. You'd then keep an eye on the weather radar, and if there was a hint of a thunderstorm on your final approach route then you'd discontinue the approach, knowing that you can hold off for maybe 20 mins and await better conditions, and if there's still no improvement, you can divert to your airfield of choice, knowing that if even this doesn't work out as planned, that you have a final reserve to fall back on. There are a lot of buffers in the system which generally ensure that it's a calm decision making process, and the core driver is an aim not to fly an approach through the dangerous bit of a storm cell.