If you connect your calendar to the Doodle app, you will see you own calendar appointments when you participate in, or create, a poll. Due to technical reasons you can only connect the local calendar of your phone, and none of the calendars you might have connected to your account on the web. The app can only access the local calendar of your phone.
However, you have to make sure that the local calendars are shown when using the app.
You can choose the calendars to show by tapping on your profile picture in the top left corner of the screen. Then under "settings" go to "calendars.” Select the calendars you want to connect to the app.
You can choose the calendars to show by tapping on the three horizontal lines in the upper left corner. Then under "settings" go to "calendars". Select the calendars you want to connect to the app.
If you want to sync the final date with your calendar, please participate using the desktop version. Alternatively, you can subscribe to the Doodle ICS feed in your local phone calendar. You can find your Doodle ICS feed here (using the desktop version): https://doodle.com/settings/calendars