It's possible there may be a problem with the site itself, or the browser. What you can do is to rename the .bin file to the expected filename. e.g. If you downloaded music.mp3 and the browser renamed it to anotherfilename.bin, just rename it to music.mp3 using a file manager.
You could also try other browsers. Give Dolphin, Boat Browser, or Opera a try and see if you still encounter the same problem.
This issue is caused by the fact that the Android Chrome browser doesn't understand UTF-8 encoding. I was UTF-8 encoding the file names since the desktop version of Chrome requires this. It turns out that file names don't need to be UTF-8 encoded for non-ascii characters for the Android Chrome browser. I was able to successfully download a file using Android Chrome with Korean characters in it without encoding it with UTF-8.