This "integration" between vim and tmux seems like a misfeature. It is poorly thought out and I'm not surprised it could exhibit such a bug. I don't want tmux sending input to vi based on an unrelated action. Just as I wouldn't expect it to know what program was in the foreground and make lots of assumptions about how it works.
Put another way, there are a lot of tmux users who take advantage of it for its terminal pane management features on a local environment rather than the classic remote-session stability use case ala screen. In that light, some kinds of integration make a ton of sense.
These days, it vaguely annoys me that I can't just navigate between OS (macOS, here) windows by keyboard just as seamlessly. I haven't quite gotten around to solving the problem with Hammerspoon[3] yet.
[1]: https://github.com/christoomey/vim-tmux-navigator
[2a]: https://github.com/jwhitley/dotfiles/blob/master/.tmux.conf#...
[2b]: https://github.com/jwhitley/tilde-local/blob/master/local/bi...