To avoid rutting or wheel dents, and depending on whether it was a "hot mix" (way too hot to touch out of the truck) or "cold mix" (maybe 100 degrees F or less), should not be driven on at all for 1/2-1 day for hot mix, 1-2 days for cold mix. No parking for 2-3 days hot mix, 3-7 days cold mix depending on mix design and how compacted it is.
Since you say only a few days before they come, I would make sure they can operate without getting on it with more than foot traffic or maybe wheel barrows, or postpone a week or more. And heavy equipment should be kept off it as much as possible anyway and not sit on it for any period of time - will scratch and gouge it or possibly dent it, especially if a loaded dumptruck sits on it for more than a minute or so. Skid-steer equipment like a bobcat can scrunch up the surface of years old asphalt, so it should be kept off totally if possible, or limit to straight run to get to the other side maybe. Ideally, put down plywood for equipment to run non if needed. This is why paving is commonly one of the last things done at a new home - to prevent damage by other contractors, and the landscaping guys are veary commonly the biggest problem (along with painters and tile and masonry contractors cleaning equipment and brushes and such and staining the drive).
Unfortunately, landscaping contractor may not agree to the delay or move your date way down the schedule. Also, if his equipment is supposed to stay off it, get that in writing - and get some pieces or lath or such and survey ribbon and mark it off so it is clear they are to stay off.
