By default, TPM installs plugins in a subfolder named plugins/ inside
$XDG_CONFIG_HOME/tmux/ if a tmux.conf file was found at that location, or
inside ~/.tmux/ otherwise.
You can change the install path by putting this in .tmux.conf:
set-environment -g TMUX_PLUGIN_MANAGER_PATH '/some/other/path/'
Tmux plugin manager initialization in .tmux.conf should also be updated:
# initializes TMUX plugin manager in a new path
run /some/other/path/tpm/tpm
Please make sure that the run line is at the very bottom of .tmux.conf.