WPML language selection

I’ve been struggling with WPML and The Events Calendar, but not in a common way, it seems.

I’m having no problems at all translating events, and the translated text and venues and so forth for events appears correctly depending on which language the user selects. Great.

But the main text of the plugin – the words for days, months, and all the rest, does not change when the user changes language using the WPML language switcher.

Before installing WPML, if I select the language in question as the admin in WordPress itself (Settings > General), then as well as the language of WordPress itself, The Events Calendar language also changed, with the correctly translated words for days and months etc appearing.

I know that The Events Calendar has an .mo/.po that comes into effect when you change language in WordPress itself. I also know that WPML has something called String Translation, which is used when the WPML plugin is installed.

What I cannot figure out is how to make these two things work together. There’s no way I want to re-translate something that’s already been translated.

I am starting to wonder if the days/months things actually came from WordPress’s language file rather than The Events Calendar’s? The language in question is Welsh (Cymraeg).

I’m sorry if this is more a WPML question that the TEC question, but I’m a little lost and I could really do with some help please!