Have you used anhydrous $\ce{CaCl2}$, dihydrate $\ce{CaCl2 . 2 H2O}$ or hexahydrate $\ce{CaCl2 . 6 H2O}$ ( 3 most common forms) ? It is a big difference in the resulting thermal effect.
Hexahydrate causes cooling down of the solution while being dissolved. If ice is used instead of water, as the mixture hexahydrate : ice 2 : 1, it forms the famous freezing mixture, cooling itself down to $\pu{ -50 ^{\circ}C}$.
Anhydrous calcium chloride causes heating up while being dissolved. It is because of releasing energy of ion hydration. Rather then smoking, it was condensed water vapor.
Dihydrate is somewhere between, with roughly neutral thermal effect.
Interaction of the group 2 element chlorides with water is generally safe. There is very slight hydrolysis, growing progressively upwards along the group. The beryllium chloride hydrolysis is significant, releasing hydrogen chloride. Note that barium and especially beryllium are poisonous.