Just a small correction, there are two letters 'љ' and 'њ' which are single char in Serbian Cyrillic (like everything else) but 2-char sequence in Latin: 'lj' and 'nj' ('pollution' and 'new'). So there are some complications when automatic switching between alphabets because it's not a simple 1:1 for all chars.
Fun fact, since both alphabets are tought early in school and used all the time, most adults can read both of them and even switch mid-sentence without noticing a difference. This also means that we're a bit "blind" about traffic signs or directions/instructions which are in Cyrillic only - we don't notice anything strange but it's a big difference for foreigners!
This is not limited to Serbia. For instance when travelling to Greece it's much better if you know how to read Greek alphabet since not everything is presented in Latin.
A small correction to your correction: The letter 'nj' is actually a single character in the Croatian/Slovenian and Latinized Serbian/Montenegrin/Bosnian alphabets (go ahead and select it with your cursor!), as are the letters 'lj' and 'dž'.
While they are certainly digraphs, they are regarded as a single letter and not a 2-character sequence. They have their own sound, sort order, Unicode designation, and written orthography. For example, on advertising where a word is written vertically, 'lj' will not be separated vertically, and a hyphen never separates the 'l' from the 'j'.
However, since the letters 'n' and 'j' already exist on a keyboard, it's easier in this electronic era for people to type the letters separately instead of hunting for the 'nj' key, so the presence that you see of two character sequences to represent those letters is a consequence of the compromise of modern electronics and expediency, not innate to the alphabet itself.
TL;DR: Each letter in Serbian Cyrillic maps 1:1 to a single letter in Gaj's Latin alphabet, as each alphabet was specifically designed such that each character represents exactly one phoneme.
This reminds me of being taught that "ch" and "ll" were a single letter each in Spanish back when I was in school before they were re-digraphed in the late '90s.
Adapting alphabets to languages has a long history: just look at how the Greeks butchered the Phoenician writing system with weird concepts like "vowels" and "F". This is something that makes languages unique, and it should be chosen over having digraphs or diacritics.
Fun fact, since both alphabets are tought early in school and used all the time, most adults can read both of them and even switch mid-sentence without noticing a difference. This also means that we're a bit "blind" about traffic signs or directions/instructions which are in Cyrillic only - we don't notice anything strange but it's a big difference for foreigners!
This is not limited to Serbia. For instance when travelling to Greece it's much better if you know how to read Greek alphabet since not everything is presented in Latin.