Nah, don't worry about action center. Go to Control Panel, Windows Defender, and just make sure that "Real time protection" is enabled on the Settings tab. If it is, it's on. Defender doesn't sit in the system tray like it did in windows 7, so don't use that as a basis of determining if it's running.
I'd also make sure you have a malware scanner installed as well. This is probably MORE important than the virus protection. I recommend Malwarebytes. That's pretty much the go to for malware protection. Malwarebytes paired with windows defender is perfectly fine as a protection scheme as long as you keep the definitions up to date.