Light the countertops, not the walkways. 1 over sink, one over the DW countertop area, 2 over the working edge of the island. Pendants aren't often enough for good working light. Lights over the walkway at the fridge/pantry area, but about 12" or less out from the fridge. Similar for the back shelving/hutch unit behind the island.

Lighting can be divided into task, for areas like counter, sink and range where you'll be prepping food. Ambient for general lighting. And accent/decorative like pendants. Task requires at least 450 lumens at the counter, not at the fixture. The puck lights your contractor likes may require two offset left to right and located 6 inches in from the edge of the counter. That'll keep you from creating a shadow with your body on your work. You need task lights over the island too. That may be your primary work zone.

Oh, just noticed that you said disks. Really don't recommend them if recessed lights are an option. We have one disk in a hallway where a duct makes recessed lights impossible. It's definitely more glare than a recessed can. I would not want that kind of lighting for a work area.

Flush LED disk lights are not really recessed lights. They throw a wide diffused light instead of a narrower focused lght.

All electricians love lights that don't require a preinstalled housing. What is it YOU want?

CAREFUL! This comment is bordering on not being a compliment and the OP might learn something! lol