First of all, NEVER answer one of their questions until start time. Many sups try this crap because their boss has given them so much to do. Too bad; that's their problem. "I'm not on the clock." Remember that. Repeat it to them a few times and they will know not to approach you before your start time.
After start time, there a few quality ways to deal with a nagging supervisor. But the most important thing you have to remember is this: remain cool and calm. I can't tell you how many sups I've known through the years whose main tactic was getting people angry. I think this is something UPS trains their managers at prick school. Don't fall for it. Cool, calm and collected. Even if you aren't dealing with a hothead, you still need to keep your head on tight. Many sups will try to make you angry because they like to argue. My current feeder manager is this kind of guy. His main tactic is trying to make us mad. Then, if you cuss back at him, he will threaten you with disciplinary action for using abusive language. True story. On the flip side of that, and this goes for a lot of sups that are like this, they tend to flip out when you talk in a quiet monotone voice to them. Especially when you have facts on your side. Again, my feeder manager is this kind of fellow. A true unprofessional.
Back to you, one way to answer their questions or complaints about the job you are doing is simply playing stupid. This is usually pretty effective if you sell it right. A few years back, I completely frustrated my driver sup, who was irritated that I kept going over 9.5. He asked about it, and I just kind of went diagonal on him. He asked why I was over 9.5, and I told him I got home at 8:30. He looked puzzled and asked again. I told him that I thought my pick-up pieces were unloaded before the sort was through. Again, he scratched his head, and repeated his question. I, in turn, asked him how hard he wanted me to work throughout the week. I think you get what I'm saying. Stupid is good in this case.
Another way, is point out the exact wording of Article 37. "The employer shall not in any intimidate, harass, coerce or overly supervise any employee in the performance of his or her duties." Tell him or her that you feel that they are violating this section of the contract. If they push further, then get your rep, and make the sup document what he is saying to you. You should also make a note of every instance that you were harassed. Note the date, what was said to you and who said it. This will help later down the line if you need to file a grievance.
I never did it in package car, but in feeders, I keep a notebook and I write EVERYTHING down. Any delays I have, however small or brief, I write it down. If the weather was rainy and I couldn't drive my normal speed, I write it down. If I had a problem with my equipment, I write it down. You don't have to be that detailed in PC, but it wouldn't hurt to jot down any problems you had each day. You know how it is, there is always some hiccup in your day. And management loves to ask you what happened 3 or 4 days ago. Well, how would you know? The days roll together. But with my book, my sups know I have an answer when they ask. Accordingly, they don't seem to ask me about the details much anymore.
I've went on too long here, but just remember, keep cool. Don't be intimidated. And always tell them, "I'm doing, and will continue to do the best I can."