Well, it depends on your definition of Space Filling Empire.
- "Very few Russians"... true, most of the time.
- "Many still "free" native tribes"... that's not that obvious; maybe closer to the Arctic Ocean, maybe deep in the forest; but mostly the Russian tsar made it perfectly clear who was in charge there.
- "The Tsar hadn't control about most of his claims in the East"... Actually he had. The population paid tribute (or taxes, whatever you call it). It was mostly in kind, not in money, I mean. It depended on what any particular region was rich with, but mostly furs.
Extracting tribute from the tribes is control in my book.
Right, it's complicated. Not only is what you pointed out relevant, but:
1. Russian servicemen and those of native stock entering Russian service (local aristocrats entered regular Russian armies as privates and officers all the time) were paid salaries in goods on a regular basis from the very beginning, so the level of government involvement is badly underestimated in the common understanding.
2. Borders were (once again, from the beginning and into the late 18th c.) contested militarily by the Khanates down south who also would have liked to collect the yasak but were successfully defended by the Russian cossacks and regulars, so the presence wasn't as ephemeral as suggested.
3. The Qing acknowledged those borders, as did the Koreans obviously. The French, British and Americans needed some persuasion in the 18th c. regarding the Far East and Russian America but they seemed to have acknowledged it too.
4. The Russians explored and mapped the entire region pretty thoroughly by the end of the 17th c. and contacted all the nations inhabiting it. It took quite a few expeditions that like, froze to death or mutinied into incoherence, but they did it, which is more than can be said of many other colonising powers in their own claims at the time.
5. Trade: from the mid-17th c and onwards there was a good deal of trade happening, totally new (overland and long-distance) trade routes being established. That is also a sign that your presence is solid enough for the market as well as foreign governments to take note.