Please let us assure you that PDF Expert for Mac is definitely an app from identified developers. The message you see might be connected with the fact that Apple removed the option "allow installation from Anywhere" during the macOS update.
In order to resolve the issue, please try the following:
- Open System Preferences > Settings and Privacy > General > Make sure that PDF Expert is allowed there.
- You can make PDF Expert a default app if you right-click on any PDF file > choose Get info > Open with PDF Expert > Change all
- You can also use the following option to open a file: Right-click > Open, Alt + double-click.