Kids can get just as anxious in a cyclone as adults can. They are very perceptive. How to help them before or after a disaster? Stay as calm as you can, and try not to over-talk your own anxieties in front of your children. Kids do not need to know all the adult stuff of disasters.. So this may mean turning the tv off at times, inundating them of information and media dramatics before or after only leads to more anxiety for children.
Your children will ask you questions so answer them honestly and as best you can. Tell them what to expect, tell them what you have done to prepare. However do not promise that everything will be okay, say something like “we have done everything we can, we will see what happens”. Afterwards be sure to not leave your house until authorities tell you to do so as there can be so many dangers for children.
I recommend asking your children how they are feeling about the cyclone .... they may be fine, they may be anxious. It is really important that if they tell you they are anxious to not dismiss it and say “oh don’t worry” instead try “it is okay to be anxious, what are you thinking about?” then listen to whatever they say, and then try to give them a little information... if they are worried about their pets then listen and say what you have done to keep them safe. They could be worried about their friends, their belongings, damage to their house, their toys. Do you best to reassure.
Try to stick to their routines as much as possible because routines brings security and comfort. However if they need to be with you more than usual, make time for them, or if they need to sleep in your room or bed this is okay too. In times of stress we need more comfort and touch. Keep them busy with drawing, writing and board games.