Being black and white in conversations, help?

I feel I am struggling with one direct and at this point I'm not sure if it's me or the direct. I feel that I'm fairly clear when i talk with this person. This person is a younger supervisor. I try not to sugarcoat things with this person but due to the emotions they bring to our meetings I do have to try to baby this direct through tough discussions.

Recently, we asked said supervisor to come in early because we were understaffed. The schedule manager and I discussed that this person may get into overtime and if things get quiet this person may be able to go earlier in the evening. Before I left for the day I told the supervisor that if everything gets wrapped up, is completely done and it's quiet (we work in a customer service industry) you can leave a little early. I never stated a time to this person because being that this person is a supervisor I would figure they would use best judgement.

At closing my superior contacted me to ask if I allowed this person to leave early. I explained the situation and asked what time did the person go. They told me 3 hours earlier than our closing time. This stunned me because knowing what type of day it was and the responsibilities involved in the role, the supervisor should not have left that early.

The above is just a prime example. Since I never stated a time, I felt that being a supervisor this person would figure it out that they were originally scheduled until 9 PM, we asked them to come in early - they agreed, but being that it was a hectic day, probably will not get out until maybe 8-8:30 if they are lucky. We never changed this person's schedule, just asked them to come in earlier. It would be their responsibility to try to get themselves out a little earlier if even possible.

I'm looking for some advice, as I need to explain all this to my superior next week but I also feel like I need to change something with this supervisor. Am I lacking being black and white? Should I be more clear give defining times to this person? Part of me thinks yes but then the other feels that being a supervisor you have to make sound judgements based on your team and how the day is. (maybe this person is lacking this skill?) Earlier in the day this particular supervisor was venting to me about never getting a "break" that they don't have any time to themselves and they are working all these days - days which the supervisor agreed to. My other concern would be is the supervisor throwing me under the bus so that they could get some time off?

What's your take? How can I be more clear? What am I doing wrong?