Quoting the rule book:
If Japan attacks any Soviet-controlled territory that is adjacent to any Mongolian territory, all Mongolian
territories that are still strict neutral or pro-Allies, or have joined the Allies as a result of a failed Japanese attack, are placed under the control of the Soviet Union at the end of Japan’s Conduct Combat phase.
So technically speaking, they first become pro-allied as Japan attacks them, and then become Russian.
On a side note, I suppose that the Mongolians would remain neutral when Japan attacks a bordering territory that was originally Russian but is now no longer held by the Russians. For example: Germany takes Moscow, and a German tank drives all the way to Amur, capturing it. Next, the US captures Amur from the Germans. And then, Japan attacks the Americans in Amur. I think the Mongolians would remain neutral in that (unlikely) sceanrio.