Somehow, the Rocky Mountains are becoming something akin to the Berlin Wall in the 19th century
Replying after the author's own response to this but before reading the next canon post:
I don't see much of an analogy at all.
1) One might stretch a point to say absolutist Tsarist Russia and parliamentary-empirically-liberal KNA are ideological foes, but this has no real traction. OTL between 1776 and 1917, Tsarist Russia was a diplomatic friend of the even more radically liberal-democratic, even revolutionary, USA. Acerbic criticism was not entirely lacking, but by and large the two empires (naming the USA as such in geographic sweep at any rate) had essentially no conflicts of interest in any concrete sense--perhaps if they had not been persuaded to give up the whole Fort Ross thing before the USA took California, there might have been some strain. But in most of the 19th century, Russia and Britain saw each other as basically enemies, barring the need for alliance in the anti-Napoleonic coalitions, and the USA had an Anglophobic streak (which is far from saying the nation as a whole was deeply antagonistic to Britain, but diplomatically speaking we would not form close alliances with Britain). This was good enough for good relations between St Petersburg and Washington. In this ATL, we have of course a much larger and actual rather than potential territorial conflict of interest, but the author is correct to note how tenuous the Kingdom's reach is into the far west at this early date.
2) If Russia were Roman Catholic there might be more of a problem, but while the Eastern Orthodox branch of Christendom (technically, even, Catholic) is pretty different from any of the flavors of Anglicanism, High Church or Low Church, there has always been, at least since the English Reformation, a weird affinity I notice between the Anglicans and Russian Orthodox. This has been something I observe in rather tenuous and symbolic forms rather than any deep meshing; in fact with substantial Orthodox and Anglican congregations in one community I believe the lines will emerge between them that sheer distance and a romantic patina never drew in OTL Britain--despite the political animosity!
There won't be a serious sectarian problem with Russian Orthodox individuals forming communities under the British crown, unless either religious fanatics seek to manufacture one, or perhaps theTsars get over-aggressive and try to turn the Orthodox hierarchy on the "Jonathan" side of the border into some sort of overt or covert branch of Tsarist authority.
3) The character of the persons filtrating eastward strongly works against the Tsar thinking he can use them in such fashions, on any pretext, sacred or secular. Unless the "Jonathans" on the spot or in Manhattan react with quite a lot of xenophobia or bigotry, alienating these new voluntary subjects of the King, they ought to fit right in in the more liberal and propertarian KNA order. If any inherent trouble comes from them, they are hardly to be feared as some marching horde of Eastern despotism--the bigger risk is they are rather unruly types veering toward outlawism. But I imagine a great many of them will compromise with taxation they think is more reasonable and comply with a state that protects their right to enjoy the wealth they dug up with their own hands. As they learn English, they have the stuff of becoming excellent subjects; their children ought to be as patriotic as any Eastern "Anglo-Saxon" Jonathan.
4) so you refer rather I guess to the Russian attempts to keep their people in as being similar to people sneaking across the Iron Curtain borders to the west in the Cold War periods. But as others note, it is not the Tsarist colonial authorities' best interest to press this point too far; it is one thing to maintain a general "Russians for Russians!" mentality in drawing on the Russian settlers to keep out greedy Jonathans from piecemeal or wholesale expropriation--but what military force they have is based mainly on this grassroots militia, not on any great armies maintained on a European scale. The Tsarist pickets, such as they are, are as interested in keeping Jonathans out as keeping Ivans in! Anyway if the will existed to try to seal up the borders and catch every footloose miner with a stake in off the books gold sewn up in their vest, good luck trying!
Not quite as impossible as merely measuring the OTL length of the region's US state borders might suggest, though, come to think of it. The Sierra Nevada mountains are quite a barrier actually; the one good pass into the Russian northern California holdings is the Donner Pass route. Do Russian claims, and actual border forts set up, reach as far as Lake Tahoe? If they do, the Russians are sort of poised to seize major parts of OTL northern Nevada, including such silver mining sites as Virginia City (again OTL, I have no idea what that town might be named here). But even if they claim the whole shoreline of Lake Tahoe, but agree with the KNA on a hard border leaving the Kingdom OTL Washoe County and points east, they do have anyway the potential to get a good grip on all the good routes out of their zone into Manhattan's claims. I believe other routes through the Sierras are possible, but not very good. To be sure, gold travels well, if the routes are not beset with bandits.
I actually think that most Russian subjects absconding eastward wouldn't get out totally unobserved by Tsarist authorities. What could be happening instead is bribery; the soldiers and even officers commanding them probably are not highly paid, and as the author notes, inflation runs wild in Tsarist California, so pay that might be respectable in Russia might be practically working for free in California at this date. If the people seeking to settle under KNA rather than Tsarist protection want to get out, perhaps they should slip some of their gold to these officials who then pocket it--and provide actually useful protection for travelers who paid this cumshaw going up the Donner Pass to the acknowledged border. This thus amounts to an alternative tax funding the Tsarist forces on the eastern border. The higher authorities might be blissfully ignorant, might suspect but realize trying to prove it is happening would be a recipe for serious trouble that would not end well, or might develop a sort of de facto shakedown--purporting to be investigations of irregularities, discovery of minor violations paid for with fines supplement getting the officers and soldiers to disclose some of their bribe income claiming they mined it themselves, and paying the full tax on the declared amount.
5) in the long run, since the threat of KNA buildup of serious force projection westward seems liable to be slow enough that evolving Russian settlement and development would outpace it (at least until the Jonathans build a transcontinental RR or two, which must be decades off at this point), assuming the agreed on borders of Russian power (pretty much the ridgeline of the Sierras I believe, the Russians controlling the whole Central Valley but not south over the Tehachapi Mountains) stabilize, the big wild card for the Tsars seems to me likely to be Russian American independence movements--but that is something they can't contemplate at this early stage. I think the Tsarist authorities will find that Russian colonists will tend to evolve an individualistic, proto-democratic and liberal leaning variant of Russian society. A day may come when, after considerably more development of the region (San Francisco bay on north--I figure the Russians are settling the Columbia/Williamette river systems and Puget Sound including OTL Vancouver Island), second, third or fourth generation Russian-Americans might decide to toss their allegiance to St. Petersburg aside, declaring a republic or electing their own Tsar. Possibly Romanov authorities can foresee this and take steps to secure the loyalty of sufficiently strong Russo-American interests, or (perhaps much enriched versus OTL by American possessions) project enough loyal enough reglar Army and navy power to deter any such thoughts. Maybe if these measures are only partially effective, the Russo-Americans might turn to KNA as protector and cut a deal of autonomy for this protection,
I think the way to bet though is that the Russians shall hang onto whatever they currently claim anyway.