On the basketball team here, our coach has set high consequences for tardiness to practice. If anybody is late, we have to do painfully taxing sprints for each minute that person is late. It has produced a culture where everybody is on-edge about showing up on time. This is undoubtedly a wise move by our coaches, as it stimulates efficiency and ensures that if somebody is late once, it is unlikely to happen again.
But on the individual level, one of the results of this strict policy is that every other situation of being late has lowered in priority. Lunch at the dining center? It wouldn't hurt anybody if I was late. Class? Nobody will care if I'm late. Work? At least if I'm late there, my boss won't make everybody else go out to the parking lot and do up-downs. If I am late anywhere else, the consequences pale in comparison to practice. The result is that I'm finding myself snoozing in the morning more and more, and arriving to commitments later and later.
In psychology this consequence for tardiness is known as positive punishment, because a stimulus (having to run) is added in order to deter team members from lateness. And it seems that when you remove that stimulus, the subject show up late more often, because the direct punishments for lateness have been removed. At least, that is what you would expect from a rat in an experimental design.
But if we as humans fancy ourselves on being more in control of our actions than rats, which I think that we do, we must overcome these outside forces. Other people may reward certain actions of ours, or punish certain other ones, but the true decision-maker will reject these outside stimuli. If you value being on time, then you should be on time for everything, regardless of the reward systems in place.
If you want to get something done, then you should set your own standards.