The setting for Synchronization at startup (under General) is checked.
Validated by shutting down my PC, sending a message from my phone to myself, waiting 10 minutes and restarting my PC. The message did not show up until I manually Refreshed.
eM Client will automatically check for messages within a few seconds after opening the program as long as your internet connection is working 100% and nothing else is blocking it
Before opening eM Client, check you can browse websites ok with no problems.
Also go to your webmail via the browser and make sure you can login to your mailbox ok with the same username and password as you setup in eM Client.
If you can login ok to your mailbox ok remotely via your browser but em client is not connecting when opening the program even after rebooting your computer, then you may have another program blocking or interfering with eM Client.
Programs that can interfere with mail clients are eg: optional Firewall / Security programs, Optional Antivirus scanning programs, Vpns etc. So if you have installed an optional programs like that, try completely disabling those to test.