If you do simple math from the year of Praxis' explosion (2293) and detract 29 (because at the time, Tuvok was 29 years old according to episode 'Flashback'), then according to this, Tuvok was born in 2264.
The episode in which Janeway gives Tuvok a birthday cake was called 'Fury'(Season 6, episode 23).
Since Voyager was launched in 2371, 'Fury' would have taken place in 2376 given that the earlier episode Muse has a stardate of 53896 (and Unimatrix Zero is the last episode in this season which has a stardate 54014) - there are 2 episodes between Fury and Unimatrix Zero (not enough time to place Fury in 2377).
That would make Tuvok 112 years years old in episode 'Fury'... and 108 years old in episode 'Meld'.
So, in this instance, Janeway seems to be wrong... and Tuvok's statement that he's been studying violence for over 100 years is accurate.
Not sure why he never corrected Janeway... but it could have been simply for the purpose of continuing to keep her in the dark.
After all, she implies in 'Fury' that it took 'exhausting research' to find out his age, and he wasn't exactly forthcoming with this data with everyone else (which is odd, considering that his SF record would have likely had this information).