@Aktiffiso, although what you've described has not happened to me personally while using Emsisoft Internet Security, it has happened to us here in our home with other AVs. On an older Vaio lap top, the action center has has told us Norton was not working, and the computer was not protected while Norton said "All systems are working & protected".

Even on my wife's newer HP system, Action Center has said protection was "off" While Windows Defender indicated it was ON.
Additionally, Voodoo Shield has alerted us (on the Vaio lap top) that it was not working (this happened at startup) and were prompted to restart to be protected which is what I recommend doing.
In my opinion, no, you are not paranoid. We always want protection to be "ON". On computer systems with many different types of software, it is always possible something just isn't working at any given time.
Fortunately you have simple solutions such as restarting. You can go further by uninstalling, and then reinstalling your Emsisoft software too. Be certain you have your subscription key if you do this.
Hopefully, it shall prove to be just a temporary hiccup which will go away with the usual updates & vigilance. If not, there are many bridges you can cross when that time comes.
Good luck!