Updating apps don't cost anything. If they have iOS devices, they're probably making in-app purchases. Many apps, particularly games, are free for the base game but charge for additional features such as levels, "coins" and other such add-ons. To prevent this from happening again, turn off "In App purchases" in the Restrictions settings on your device. You may also want to turn off the ability to install apps, to prevent purchases in case the child gets hold of your iTunes Store account information, and set the password to be required immediately. For more information, see:
As to changing your account information, see:
but I'd suggest just setting up the parental restrictions on the iOS devices and in iTunes on your computer, if applicable, so they just can't buy anything on their own.