I do not have a DB20-G, but I think I know the answer anyways so I downloaded and installed the Radioddity CPS, which is very similar to the software for a number of other Chinese radios.
If you are using the software, hit the ">>" under "More" for the channel you are trying to configure and it will bring up a dialog with all the parameters. Right under the "CTCSS/DCS Decode" and "CTCSS/DCS Encode" boxes, you'll see one called "Squelch Mode". Set it to "CTCSS/DCS".
If you are programming by hand, look for the corresponding menu item and change it from "Carrier" to "CTCSS/DCS".
Please let us know if that fixes the issue. If you've already done that, then I would say the firmware has a bug, since it's opening squelch for any signal (carrier) rather than only for one with that Decode tone.