Hello,

Do you mean another class/job or an actual alt (another character) ?

Whichever it is, yes, the dungeons will be restricted to the level of said class/job, or character. Even if you unlocked all the dungeons with one job, you will only have access to dungeons within your level range if you switch jobs.
As for an actual alt, so another character, they don't depend on your 'main' character for dungeons, they have to unlock their dungeons the same way you did on your main.