I've never tried using a simple A/B switch with the DT amps.  I have a POD HD500 and the POD HD PRO to control the DT amps.

Did Line 6 has post an official recommendation of a brand, a type, or a specific configuation?

If not, then I'd suggest trying the polarity of your switch, try a single TS type cable and a TRS cable.  there are a few footswitches out there that can do all of the afore mentioned things with the same footswitch.  The best I've found is the BOSS FS-6

Hope this info helps,

Neal