How are transliterated words pronounced: as they are in the origin language or according to the recipient language's rules? Say, we have a Soviet multiple rocket launcher "Buk". In Russian, the second letter is pronounced as [u], but if it was an English word, it would be pronounced as [ʌ] or [ə].
Generally, words are pronounced to approximate the pronunciation in the original language. Often there is some modification to English phonemes and sometimes the words are more mangled.
So "buk" would probably be pronounced the same as "book". Note that pronouncing u as [u] is well known in English, for example "put". Enen thought the English vowel isn't exactly the same as the Russian vowel, there are several different pronunciations of "u" in English, the transliteration of Russian to Engish "u" is because there is are words in English that are spelt with "u" that have a sound similar to the Russian.
Speakers who are familiar with Russian would normally try to approximate the Russian pronunciation better. For example, the "shch" consonant that produces such difficulty for learners of Russian. So "borshch" is pronounced "/bɔː(r)ʃt/ by most people. But people who have studied Russian will aim for something closer to [bɔrʃtʃ], and people will treat being able to pronounce more closely a foreign word as a sign of the greater education and knowledge.
If you are speaking English and there is a Russian word, you should pronounce it as it is in Russian, and not try to emulate an English mispronunciation. Perhaps if the word has been completely incorporated into English (like, for example, "mammoth") you might treat it as an English word and not Russian. But borrowings "babushka", "matryoshka", "sputnik" may all be produced as Russian words, even if English speakers will modify/mangle them.
It depends on the word and, to some extent, the speaker.
No matter what the word is, guarantee that there is at least one accepted pronunciation that uses all English phonemes. A good dictionary should tell you the most common. For frequently used words, there's often just one "correct" English pronunciation, even if it isn't the closest match the phonology has to offer.
Accurate pronunciation can be warranted if a word is being used close to its native context, which will usually be clear. I don't recommend using them far out of context just to sound "cultured," however. "I could really go for a taco from Taco Bell" does not and should not warrant a special pronunciation (yes, I've heard the likes once in a while).
There's a sweeping exception when it comes to words in your native language, though. Those are your words, and certainly no one will think it strange if you pronounce them correctly. "I could really go for a taco from my uncle's taco truck," said by a native Spanish speaker, is a whole different deal than the above. And by all means, as a Russian, claim Sputnik as your own.