Not to get technical, but "until 1:40pm" doesn't mean "through 1:40pm". "You can park here before the time is 1:40pm. Once the clock shows 1:40pm, you are over your time. You can park here until a clock shows 1:40pm."

To make it really clear, the first minute is 1:10:00-1:10:59.99999. The first minute doesn't extend until the end of 1:11. Then that would be two minutes. The first minute extends from 1:10 until 1:11, not through 1:11.

I agree that the city shouldn't ticket until 1:41 in your case because people have trouble understanding situations like this.

Imagine you're a doctor scheduling 1 hour appointments. If someone is scheduled from 9am until 10am and another person is scheduled from 10am to 11am, the first person doesn't continue to be seen at 10am. They are seen until 10am. Otherwise, the second person's appointment would start at 10:01am. Likewise, your parking goes from 1:10pm until 1:40pm. As soon as 1:40pm started, your time had expired.