The rules say this:
“Due to its separate treaties with Germany and Japan, the Soviet Union is in a unique position in its relationship with the Axis powers. As a result, if the Soviet Union is at war with Axis powers on only one map, it is still under the restrictions of being a neutral power (see “Powers Not at War with One Another,” page 15) on the other map. In other words, a state of war with Japan lifts those restrictions from the Soviet Union on the Pacific map only, and a state of war with Germany and/or Italy lifts those restrictions on the Europe map only.” (this is from page 36 of the Europe rule book)
If you go to page 15 it restricts the movement of neutral powers so that they cannot enter the territory of other powers (friendly or otherwise) until they are at war.
So soviet units must stay inside the Soviet Union on the pacific map (which includes Burma and India) until they are at war with Japan.
I’m fairly certain that this was not changed for BM, but others can confirm.