Yeah, nah. This is in New Zealand if I'm not mistaken (and it's a shitty little mall if I'm thinking of the right one) and we're all about consumer rights here.

The only way they could even think to get away with kicking you out once you're actually giving them your patronage is by serving you a verbal trespass notice (I can't imagine they would go so far as to give you a written trespass) and then record your name (which you do not have to supply them, which kills their trespass notice anyway as you can claim it wasn't you or you didn't know) and your description, plus the date and time for every offender for it to hold any weight at all if they were to push the issue further.

If they did push the issue further, the main reasons for pushing a trespass notice are, "They may be committing offences on your property, such as shoplifting, being disorderly or simply have no right to be there." - none of which using an application on your phone as you are shopping fall under so it wouldn't hold water in any kind of dispute.

Also, a single sign on one or even each of their entrances can be easily missed, so you're not falling under any contract by walking through that door that would give them the right to kick you out for something as niche as this like you would be if you, say, called a restaurant and made a booking and they specifically said, "You're not allowed to wear short shorts as this is a formal restaurant."