Many Zsh configurations by default don't work out of the box with the way the script installs the autocompletion for zsh.

Besides sourcing the tmc-autocomplete.sh file the autocomplete install script could add

autoload bashcompinit
bashcompinit

into the zshrc file before sourcing tmc-autocomplete, but only if it's not already there. This lets zsh support bash completion and allows the autocompletions to work.