@thor The Cyrillic alphabet's "И" is actually just "i" as in "fish". If it were "Putjin", then the spelling would've differed: "Путьин", where "ь" serves as a separator that also palatalises.
So in "Putin" there are just 5 sounds.
And in "нет" ("njet") – 3 sounds. Native speakers can tell, really.
The trick is that East Slavic languages have a very distinct difference between palatalised and non-palatalised consonants. The "t" here is very distinctly palatalised, which is close to what an additional "j" would also do.
There is also a non-palatalising alternative to "и", which is "ы" (transliterated as "y"). By of them in a sentence: "ты тихий", "ty tihij".
Also on the topic: there is a Cyrillic letter "ї", which is present in Ukrainian, that is just like the Latin "ï" (as in "naïve").