People are different. For some of us, punctuality is important and good timekeeping is a big deal. For others, not.
If it isn't a big deal for you, make it a big deal. Don't waste emotional energy on people who are late, but make sure you're not one of them. Lots of tricks and tips...
1. If you can't make it on time, say so in advance, and ask for the start time to be changed.
2. Use your mobile phone diary/alarm feature.
3. Set your alarm five minutes early.
4. Keep things (keys, pens, diary) in a standard place so you aren't delayed at the last minute.
5. Prepare the night before a morning appointment (lay out your clothes, set the breakfast table, pack your work bag)
6. Work out routes, timetables, alternatives in advance.
7. Make sure you know practical details (Room number, contact name, phone number) of any appointments.