Looks like these options are similar, but only the second one seems to work with zsh, so I added it to my zshrc file!
IGNOREEOF=10 # Shell only exists after the 10th consecutive Ctrl-d
set -o ignoreeof # Same as setting IGNOREEOF=10
Seems like another option would be stty eof undef
Source: https://superuser.com/questions/479600/how-can-i-prevent-tmux-exiting-with-ctrl-d/479614