No, you are not charged when your customers respond to your message. However, depending on whether they respond to a short code/long number, your customers will be charged at their standard network rate for text messaging.

If the sender(From) is alpha-numeric such as the name of your business or brand, your customers cannot respond to your messages. If the sender is a valid phone number, contacts can respond to the messages but these messages will not be collected in Inbox.

To see your customer replies in Inbox, you need to buy a number (Channel setup --> SMS --> Numbers --> Buy Number) and use it to receive replies.