The "Security Warning" popup is normally shown when the "Permanent Caching Mechanism" for IE+MS JVM is used. This will cause the applet to be installed locally on the client machine when it runs for the first time. Of course only if the user clicks "Yes" in the security prompt. The next time the page is visited,  the security prompt will not be shown again and the applet will be loaded from the copy installed locally.

In general, all browser will show some kind of "Security Warning" when loading the edit-on Pro applet, because our applet is digitally signed with our companies official digital code signing certificate issued by the Thawte CA. The digital signature guarantees that the applet has been created by us and hasn't been tampered with in any way. Using a digitally signed applet is necessary for a number of important things like Copy/Paste between the applet and Windows applications like Word, opening contents from remote servers, permanent caching etc. Basically, it allows an applet to get out of the Java applet sandbox in a controlled fashion.All browsers offer a way for the users to accept the certificate permanently. They won't be prompted for a second time. The issue is described in the edit-on Pro Integration Manual in chapter "Java Security Considerations"  

An unsigned version of the applet could be used to prevent the popup, by repacking the JAR, but please keep in mind that we wouldn't support that. Also it would disable features like Cut/Paste etc.