If they start barking or coming to me then returning to a person.
I don't hesitate but walk right up to the person and ask them if they have a problem with the dog. Were they petting dog when it began barking? Are they uncomfortable with dogs?
If I am the owner I am responsible for the dogs actions. I get involved right away.
There have been folks that don't like dogs and dogs know that. Folks have been mean to my dogs. Lots of things both inappropriate and not a big deal.
Don't hesitate when your dog alerts... find out what happened, etc.
Ask questions politely cause the person may not have done anything.
Be careful not to jump to conclusions without talking to the person involved and getting all the facts.
Most of the time with my dogs it was nothing but a smell of another animal. Food the person had on them. A kid who tweaked a dogs nose. Once a person terrified of dogs who just sat there scared to move.
Do step up and ask what happened. You are the one in charge. Just don't ignore the situation
Cats and horses and birds also react to people. I intercede for all of mine, past & present. Chance hates women and loves men. But women stick their fingers in the cage right away. Sheesh.... stupid as I tell them not to.
People can be sneaky, mean and not smart.
Love All Life, Thank You For Posting! :)