Because CT is supposed to be a challenge? It's not a campaign that you breeze through and JW chaos has a 5 star difficulty rating, so you should expect it to be difficult.
I played it at least three times by now and never had any issues with the storms, Rex dying or otherwise. Usually when I reach that point (if it dies at all) I already have 20mil+ in the bank and a profit of 300k or more. What you want to do is make sure you don't overpay or hire too many scientists, keep checking back with the amenities to make sure they still got max profit and upgrade them as soon as you can since medium and large ones make way more profit than small ones when maxed. And then you only want to put them where the dinos and attractions are, not where the management view tells you to or you'll loose a bunch of money.
As far as the storms go listen carefully for the thunder in the distance or the weather forecast in the park when you're close enough, then you get a bit more time to react and open shelters, close shops etc. Also use double gates so your dinos don't run free as soon as one is demaged by the storm and opens. Assign choppers to the ranger posts so dinos that pose a threat are dealt with right away and make sure to keep at least 1.5-2mil in the bank at anytime to deal with storms, then you shouldn't have much trouble with them.