Since the Russians wouldn't trust a Mexican, American or British workforce to exploit the gold fields, lest their respective countries claim the region for themselves, and since bringing Russian workers halfway around the globe if going to be quite a hassle, Russia may have to bring in Chinese workers.
A good section of the "Russian" population in Alaska was Finnish, for a big part because a major slice of Russian long-distance trade was in Finnish hands at the time. This from a Finnish genealogy site,
www.genealogia.fi:
"The second contribution of the Finns - together with the Russians - was made in connection with the Alaskan undertaking. This was begun by Russia at the end of the 18th century; but it was not till Finland had come under Russia in 1809 that the Finns had an opportunity of taking part in it. Lieutenant - later Admiral - A. A. Etholen, who had qualified at Finland's Naval Academy, served as Captain on the ships of the Russian Fur Company trading with Alaska, and was appointed Governor of that province in 1839. He took up residence there in 1840 bringing with him a Finnish pastor, Uno Cygnaeus, who afterwards became famous as the founder of our elementary school system. The fact of his going there indicates that there must have been Finns in that country already at that time, and subsequently they moved over in greater numbers.
A branch of this company, called the Russo-Finnish Whale Trading Co., was established at Turku (Åbo) in 1849 for the purpose of trading in Alaskan produce, and in the ships of this company - including the "Suomi", the "Turku" the "Sitka", and the "Atka" - more contingents of Finns, especially from the vicinity of Turku, emigrated. Etholen's executive official was a Finn, Lt. T. Bartram. The Captains of the ships were Finns, e. g. Gustaf Nybom and D. A. Grönberg, and the crews were of course mostly Finns too. Later, in 1859, another Finn - Capt. Johan Hampus Furuhjelm - became Governor of Alaska. The Finnish population in this province reached its highest number - about 500 - in the 1860's. The whole enterprise was prosperous, but the Crimean War of 1854-55 had a harmful effect on it, and finally, in 1867, Russia sold Alaska to the United States. Some of the Finns then returned to their home country, some went to the United States, while others remained in Alaska, mostly becoming assimilated with the rest of the population.
The third period of emigration was during the famous Californian gold rush of 1848-50, when Finnish sailors, especially in San Francisco, were lured by dreams of wealth to desert and become part of the motley crowd of gold-seekers."
The OTL Finnish migration to America really got going after the American Civil War, thus if Alaska and California are in Russian hands at that time, California will receive a much larger Finnish (plus Ingrian and Baltic) population than it had IOTL. In the overall picture, this is not much initially but eventually the divergence would probably bring about some interesting butterflies.