The official novelisation for the sequel indicates that the the Doc who arrives at the end of BTTF is the Doc Brown that is contemporaneous with 1985 Marty.
They would be very careful, Doc told himself, and there would be no mistakes. While he had been in the future, Doc had done some research into the nature of time paradoxes, and discovered their results could be far more devastating than he had ever imagined!
This line would make no sense if this was the Doc from the future. And
All that remained was a simple matter of logistics. Doc would pick up Marty and they would go back to the future . . . actually their own present, October 26 1985. And this time it would be the same 1985 they had left from on the morning of October 26 1985.
So it's their own shared present. His Doc is the Doc that he's been traveling with, not a future Doc (unless he's been very consistently lying to Marty).