One of two things would need to have happened for the Japanese to have attacked Siberia:
1. The Japanese back out of French Indochina in 1940 so as to remove the US embargoes and the need to "Go South." Seeing as how this would have resulted in a massive loss of military prestige, it was extremely unlikely.
-OR-
2. The German Army captures Moscow in the fall of 1941. It was informally agreed within IGHQ that should Moscow fall early they would make a land-grab in Siberia with the forces on hand. Given the Wehrmacht's inability to capture Moscow in the face of Soviet resistance and the weather, this is even more unlikely.
So, going with the most likely of the two scenarios (evacuation of Indochina), the Japanese attack on the USSR is not a 'come as you are' land-grab but a full-scale war: Hachi-Go no. 8, IGHQ's plan for an all-out war against the Soviet Union, envisioned the initial blow to be struck by up to 43 divisions and numerous smaller formations totalling 1,300,000 men. They would first attempt to cut off Soviet Primorye from the rest of Siberia (while holding a defensive posture in the West), then turn their attention to the Baikal area, halting at roughly the Yablonovy mountain range. If the Japanese had agreed to the attack with Germany in March 1941, the operation would be ready by August.
The Soviet order of battle in the Far East was huge: As of December 1, 1941, the Red Army had a total of 1,343,307 men, 8,777 guns and mortars, 2,124 tanks and SPGs, 3,193 combat aircraft, and 96 ships of various types guarding against the IJA. This constituted a very considerable force, one that looked like it might have been able to handle Hachi-Go...until one realizes that it was spread out over a vast arc from Vladivostok to Mongolia, consisted of largely second-line equipment, and had been stripped of its best officers and men for the war against Germany. Moreover, the Soviets were oriented in a purely defensive posture, incapable of making major advances into Manchuria. Even worse, their forces facing Japan were connected to the rest of Russia by only the single Trans-Siberian Railroad, which was very close to the Manchurian border and could easily be cut by aircraft or ground forces.
The Japanese, on the other hand, would be using their very best and would hold the initiative in a battle started by themselves. They would likely enjoy the element of surprise, with total air and naval superiority. Given the geography and infrastructure of Manchuria, they would also operate with a relatively compact grouping with the advantage of interior lines, and could call on their vast merchant fleet for supplies and reinforcements. It was essentially the exact opposite of the situation the Japanese themselves faced in August 1945: this time it was the Soviets who had the shell of an army.
Given these conditions it's not hard to imagine that the Soviet Far East would end up flying the Rising Sun. Resistance would be very determined and at times surprisingly painful for the IJA, but given the skill and logistics disparity the ultimate outcome would not have been in doubt: the Red Army would be overwhelmed and resistance would be reliant on partisan activity. Following such a disaster the remoteness of the theater would basically mean any serious response from Stavka would be delayed by years given the precarious situation with Germany: Stalin wasn't going to sacrifice Moscow to save Vladivostok.