Despite what it says in the docs, $EDITOR and $VISUAL do not seem to be used when they are set. This is not because GIT_/TIG_EDITOR are set and overriding them, as I do not have them set.
In my actual environment I have $EDITOR set and none of the others, but you can see this by invoking tig directly with no existing env vars:
# these do not work
EDITOR=nvim tig
VISUAL=nvim
# these do work
GIT_EDITOR=nvim tig
TIG_EDITOR=nvim tig