aCalendar is not involved in calendar synchronization. The app is just an user interface to the Android calendar storage and does not save any calendar data itself.
Synchronization is always provided by your chosen cloud service. The synchronization option within aCalendar tells Android to tell all cloud calendar services to sync. Your cloud service however should also listen to database changes and sync automatically. If not, most likely some battery saving options block it from doing so.
For Google Sync Issues please see: Problems with Google Calendar Synchronization
For Exchange Sync Issues please see: Microsoft Exchange (hotmail, Microsoft 365, Office 365, live.com, outlook.com)
For CalDAV calendars please see: CalDAV (Owncloud, Synology, Yahoo, etc.)
For One Plus Devices please see: Issues with One Plus Devices
For Xiaomi Devices please see: Issues with Xiaomi devices
For shown error codes/ messages please see: Synchronization error codes and messages
Steps to do:
- If you have no synchronization between 2 Android devices (e.g. phone and tablet), you should first identify which device is the problem. Test each device individually to the web interface of your chosen cloud service (e.g. Google calendar in a web browser: https://calendar.google.com).
- Then check your Android accounts/sync settings.
This setting is also linked in the aCalendar 'calendar list menu'.a. Open the MENU
b. Open 'Manage Calendars'
c. Open the calendar list MENU 
d. Open the link 'Android account/sync settings'
- Check your global sync settings of your device.
- Check your (background) data settings.
- Check your energy saving options.
- Please see also the service-/device-specific help pages here and the help/support pages from your chosen cloud service.