I'm not a tree guy but this advice comes from 30 years in the building trades. I think there are some parallels:
-Start time isn't when you show up. Start time is when you have all the tools and materials laid out and you are working. So if you are told, "We start at 8 am" you need to account for travel and set up time. Quitting time works the same way. And don't tell your boss when it's quitting time. He will tell you.
-Always be busy. If you don't know what to do, ask. But don't be afraid to be a self starter. There is always something that can be cleaned up, put away, made ready, etc.
-There is a fine line between being ready to help vs getting in the way. Sometimes people can be rude about it. You might get yelled at. Don't get discouraged. Stick with it and you will figure out the workflow. This is part of paying your dues. If you are the guy who stands around waiting to be told, the crew will come to resent you. If you are the guy always ready to lend a hand, they will come to respect you.
-Leave your phone in the car if you drive yourself to the site. Leave it in your lunchbox if you are driven by the crew.
-Be vigilant about safety. Not just for yourself but for everyone. It's not just the obvious things like saws and falling objects. Look for trip hazards, boards with nails, broken safety equipment, etc. Those little details are going to be your responsibility as the grunt. I guarantee you if someone trips over a tool they are going to look straight at you with murder in their eyes.
-Remember "Quiet Coyote". Mouth shut, ears open.