Unfortunately I don’t know where the DSON support and PNG files go if you are manually moving files around, somebody else will need to answer that.
However, if you also want to get the installation process working normally, here are some things to check:
Make sure that the folder DIM is installing into is also mapped in DAZ Studio.
In DIM you can click on the gear icon in the upper right corner to get to the Settings window, then click on the Installation tab, then make sure that the path named in the “current” dropdown listed above is the one you expect it to install into.
In DAZ Studio, in the Content Library tab, click on the menu icon in the upper corner and select “Content Directory Manager”, then make sure that same path is mapped under “DAZ Studio Formats” and/or “Poser Formats”.
Once installed, select “Scan Known Directories For Files” from the menu icon to make DAZ search for your newly installed content.
At this point, your content should show up in the Content Library in subfolders either under Categories > Default > Unassigned, or placed in the appropriate subcategories under Categories > Default.
Because it may be difficult to locate if it didn’t end up in unassigned, immediately prior to installing the product you can right-click on a category and choose “Mark all content as seen” to clear all blue highlighting from every category in the Content Library, and after the new content is installed, you can just look for all the new blue highlighting to find all the scattered bits. Or another way, you may also be able to find it listed alphabetically under the name of the product under the Products category (I don’t remember the rules on when it does/doesn’t get listed in there.)