How to setup zsh with fzf history backsearch in tmux (I get zle errors)

I am using tmux with the zsh shell. I try to setup fzf, and I do it like this (inside my zshrc):

eval "$(fzf --zsh)"

This works, as long as I am not in tmux. I can use Ctrl-R and get the fzf history search. But inside tmux this does nothing. When I try to invoke the history back search manually, I get:

❯ fzf-history-widget
fzf-history-widget:zle:14: widgets can only be called when ZLE is active

A bit of googling suggests, that I need to load zle first, but also:

❯ zmodload zsh/zle

Does not work. What is wrong? What can I do? Edit: As requested, here is the the output of bindkey | grep fzf:

❯ bindkey | grep fzf
"^I" fzf-completion
"^R" fzf-history-widget
"^T" fzf-file-widget
"^X." fzf-tab-debug
"^[c" fzf-cd-widget