Thanks for your response. Here a screenshot of my setting. As you can see it is the same as yours.
What I identified is, whe I change the slug in to different languages in the settings of The Events Calender, it generates a different string in the WPML String translation. Please see image below. At the and I changed the slug to Turkish .com/etkinlikler, which is the main language in our site, and in the different languages it look like .com/en/etkinlikler.