One the islands, Copper Island, is directly mentioned by name as the border was placed between it and Attu. Copper was on the Russian side.
The treaty does not list every island in the area, but uses some islands and some of the mainland to determine where the dividing line was drawn. All of those islands reside on the Russian side of the border.
Read the following description of the Western border from the 1867 treaty and tell me how any of those islands west of the border actually belong to the US:
The western limit within which the territories and dominion conveyed, are contained, passes through a point in Behring's straits on the parallel of sixty-five degrees thirty minutes north latitude, at its intersection by the meridian which passes midway between the islands of Krusenstern, or Inaglook, and the island of Ratmanoff, or Noonarbook, and proceeds due north, without limitation, into the same Frozen ocean. The same western limit, beginning at the same initial point, proceeds thence in a course nearly southwest through Behring's straits and Behring's sea, so as to pass midway between the northwest point of the island of St. Lawrence and the southeast point of Cape Choukotski, to the meridian of one hundred and seventy-two west longitude; thence, from the intersection of that meridian, in a southwesterly direction, so as to pass midway between the island of Attou and the Copper island of the Kormandorski couplet or group in the North Pacific ocean, to the meridian of one hundred and ninety-three degrees west longitude, so as to include in the territory conveyed the whole of the Aleutian islands east of that meridian.