It took me some time but I finally found out what's going on.
First of all, the isomount file located in C: needs to have "S" file attribute (also called protection bit) set. Otherwise it won't launch. Go to AmiKit:C folder, mark the "isomount" file, click the down-arrow located in upper right corner of the DOpus Lister and select Properties > Attributes and set the S protection bit there.
Now double-clicking the ISO files will mount them - until you have OS3.1.4 or OS3.2. In that case you need to do one more thing. Go to AmiKit:L folder and mark the "CDFileSystem" file, then click the down-arrow located in upper right corner of the DOpus Lister and select Duplicate. Enter a new filename "CacheCDFS" (without quotes). Now you should be able to mount the ISO files. Btw. even VirtualCD should mount them as well now.
And thanks for this bug report! I will fix this in the next Live Update.