The question 'How are you doing?' is a Pleasantry, rather than a genuine request for information, in this instance (ie the question is from a service employee rather than a friend or anyone who has a personal reason for being interested in your well-being).
: something (such as a greeting) that people say in order to be polite
Source: Merriam-Webster's Learner's Dictionary
This should help you to work out the answer in similar situations.
In this example: one would not, under most normal circumstances, respond 'I'm terrible' to such an inquiry from staff in a shop. If the ways in which you were feeling terrible related directly to something about the shop/service which you then went on to explain so that they could fix it, that would be okay. But you wouldn't tell shop staff, whom you did not know, that you were terrible if the reason was that your hamster had died.