Korean is Korean so there is no correct way to turn Korean into English.  I can’t exactly tell you which is right over the other.  My best advice would be to learn the characters with their sound instead of relying on romanizations.

To address the question though, ‘u’ can be applicable to both ㅓ and ㅜ.  In the English language, a short ‘u’ has the ‘eo’ sound like in ‘up’ whereas a long ‘u’ has an ‘oo’ sound like ‘use’.  For the sake of simplicity I would use ‘eo’ as a romanization for ㅓ instead of ‘u’.