No you’re right I missed a piece of the path.
You need to clear the ai1ec cache to get it to work.
Easiest way is to rename the twig directory in …../all-in-one-event-calendar/cache/ and then refresh the page. Rename it to something like oldtwig.
If your permissions are ok, it will re-create that dir (and all the subdirs under it) then you can delete the renamed dir (eg: delete oldtwig).
If your permissions aren’t correct, ai1ec will not be able to create the dir (probably producing an error and disabling the plugin, so you will want to rename oldtwig back to twig and then re-enable the plugin so that people can at least use your site.
Note: If your cache permissions are wrong, you need fix them so the webserver user can write to them. It should be fine though as otherwise you’d have other errors. That said, I always recommend the rename/test/delete method, as it gives you a fallback in case there is an issue.