Stalin did have plans to take Hokkaido along with the Kuril islands. These were drawn up in late June 1945. In the end, after Japan's acceptance of the Potsdam terms, he was persuaded by Molotov to abandon the idea of invading Hokkaido, because it would create a confrontation with the Americans, but he did order the late taking of the Kurils. I would consider Hokkaido part of "Japan proper" (it is one of the "home islands") — and more importantly, both Stalin and Truman considered it to be such. Stalin later asked Truman for an occupied zone in Hokkaido, and Truman denied it, on the grounds that it was "Japan proper."

I have never heard of any joint invasion plans. All of the above seems to suggest clearly there was no real joint coordination. By the time of Potsdam, the US was souring on the idea of Soviet occupation of Japanese territory, because they were learning from the experience of Eastern Europe that once Stalin possesses territory, he does not easily un-possess it. In any case, the US wasn't even sure when the Soviets would declare war, and thought it was going to be mid-August, not early August — this was one of the factors in the timing of the atomic bombs, to hope that they might pre-empt the Soviets. So clearly no real coordination was taking place; I am not sure any was contemplated.

Hasegawa's Racing the Enemy has a lot on the above, and is what I consulted in refreshing my memory on the Hokkaido plans.