Yes. The firmware will display the box model it was written for, but it's compatible with the older boxes as well. Only the latest boxes (with the channel 3/4 switch) are incompatible with V13.
If you still have the remote that came with your 3500STB, you'll find some of the buttons don't function as labeled with V13. The 3500STBII's shipped with the new remotes, a few of the buttons are different, and the V13 firmware was written for the new button layout. If this bugs you, you can buy one of the new remotes from iView for $10 (free shipping). You'll probably like it better anyway.