But I actually found out how to download links using IDM through Maxthon in several simple steps.
Here is it:
Let's download a link in Mediafire for an example.
When the download link appears, right click on the link and select "Copy Shortcut"

Then a pop-up from IDM will show up.
Click "Ok" and there you go!

Simply the reason for this is that IDM had capture a link to download when we copy the link.
Hope this helps!