That is behaviour by design - Each Set List is a "Bank" in the MIDI world which is an independent set of MIDI Patches to cope with devices having more Patches than the MIDI standard allows. Within each Set List the HD POD sends Patch Change = 000 for Preset 1A, 001 for 1B, etc. You can send Bank Change messages to move between Set-Lists.
According to the PDF manual the Fender has:
The presets are organized into 3 banks:
C00-C84 - FENDER CUSTOM SHOP: 85 Premium amp and effects combinations stored in permanent memory.
P00-P84 - PLAYER’S LOUNGE: 85 rewritable presets for your original Amp designs. FENDER CUSTOM SHOP presets are saved in these locations as place holders until you want to change them. These presets can be reset to factory default in the UTILITY Mode.
A00-A34 - YOUR AMP COLLECTION: 35 of the greatest amp circuits of all time, the way they left the factory, stock-equipped.
So it has 3 "Banks" two of 84 Patches (presets) and one of 35.
FENDER CUSTOM SHOP Bank #01: C00 – C84
PLAYER’S LOUNGE Bank #02: P00 – P84
YOUR AMP COLLECTION Bank #03: A00 – A34
It also says:
Any MIDI program changes contained in bank #00 can be mapped to any preset on the Cyber-Twin. Two of the FX knobs are used to select the values in this menu. The FX LEVEL knob selects MIDI program change numbers 0 - 127 and FX VAL2 selects the target preset for control. Only MIDI program changes in bank #00 will access the MIDI Preset map.
So it doesn't have a Bank #0, but maps MIDI Bank zero to any Present in any of the internal Banks.
What this means is that the default midi sent by the POD for the same Preset change (in different Set Lists) will always go to the same Patch on the Cybertwin. I don't know about the FBV programming, but the HD500 can be set so that any footswitch can send any Patch Change message you want,
Personally I would restrict my HD Patches to a single Set List - 64 different virtual Rigs is enough for a single gig isn't it? You might clone that set-list to create for example Full Amp version in one and Pre Amp only version in another, or Full volume EQ'd and Quiet volumes and do the mapping on the Amp as required. I actually only have 8 patches that I use regularly anyway but with pedals that get switched in or out, and use of the guitar volume control and pickups to vary the sounds