Tickets have been reduced to just 50 cents in a six-month trial, but people are still not paying to ride buses, trains and ferries.
In the first two weeks, 475 people were fined, while almost 4,000 commuters were issued a warning.
Transport Minister Bart Mellish said it was disappointing that some people were "doing the wrong thing" despite the cheap fares.
"You might be able to get a cone at McDonald's for 50 cents. That doesn't mean you can go behind the counter and serve it yourself," he said.
"That is still theft and fare evasion is still fare evasion.
"We want to see people tapping on, tapping off so we know where people are coming from, where they're going to, how they're getting about our network."
Mellish said the number of fines and warnings handed out are on par with the number before the fare drop, and they only dropped slightly.
Between 2018 and 2022, the number of commuters hit with a fine for fare evasion was about 60,000, with an average of 288 per week.