I employ several young people all in their late teens to mid 20s. We've had two or three in the past who were constantly late, constantly off sick, always asking to either come in late or go home early for some reason, always making excuses for things. None of those three people are still with us. They were all sacked eventually for unreliability.
I have another three people of roughly the same age who are fantastic. Two out of three of them have long journeys on rural buses that are not that frequent but in the four months they've been there they've never been late once. They get in ridiculously early out of choice because they know that although a later bus would get them there on time in theory, if it was cancelled they'd be very late.
I've never asked them to do this but I hugely appreciate their commitment and work ethic and I will make sure they are rewarded for it. What is interesting is that they are generally much more conscientious and more enthusiastic in all other areas of the job than the previous set of people were, as well. They have a real 'can do' attitude instead of trying to get away with doing as little as possible.
So it's likely that it wasn't just this lad's lateness that was grating on his employer. Perhaps his lateness was a symptom of lacklustre performance in general.
That may not be true and may be an unfair assumption of this lad, but my gut feeling is I'm right. As an employer myself, if I had someone who was generally doing well I'd want to give them a chance to sort out the areas where they were falling short, especially if it was something with an easy solution. If not understanding the need to get an earlier train after less than a month on the job was the only problem, I'd talk to them about it and give them some time to correct it. They are on probation so there would be plenty more time to sack them if necessary.