This is only indirectly associated with Safari, in that if Safari is set to "Open safe files after downloading," it will do just that, based on the Finder settings for the extension of the file concerned. For most people, Finder is set to open mp3 files with iTunes, so that is what Safari does: Safari is obeying your instructions. Disabling this feature means that files with other extensions, which you might well want opened with default applications, will simply sit there, doing nothing. So don't cancel this option, unless you are willing to open every type of downloaded file manually.
What needs to be changed, then, is the default application to open mp3 files. The current application (usually iTunes) can best be found by selecting any mp3 file and opening the Info window for that file with Finder menu item File>Get Info or Cmd-i.
Look down the Info window and find the section "Open with:" (if the little triangle preceding these words is pointing to the right, click on it to expand the section). Here you will see a drop-down, probably currently populated with iTunes; when expanded, the drop-down shows other apps capable of being used for that type of file. One would also expect to find an option such as "Do nothing" or "None." Sadly, this is not provided: one is forced to pick an application and that is what is causing the problem.
There is a solution, however, in the form of a System extension that provides just the "Do nothing" option that is required: RCDefaultApp(it's free).
Although this extension looks old, I have used it successfully with El Capitan.
Hopefully, a future update to OS X will provide its own "Do nothing" option.