My understanding is that the 0db setting in preamps (that's where your display logic gets the volume setting) is a reference indication that corresponds to the RMS voltage being sent by the preamp to the amplifier so that the amp can deliver its rated power level. Typically, that would correspond to 1V RMS that is meant to drive the amp to its full rated power of, say, 100watts continuous into the required speaker load. Different amplifers have differing input voltage requirements for full power, ranging from 0.8V to 1.5V, more or less.
For some preamps, a 0db setting corresponds to a unity-gain output where the input signal to the preamp circuit equals its output signal. Any db marking above that would indicate some gain in the preamp circuitry.
Hence, the negative db settings correspond to volume levels BELOW the 0db reference. And if the preamp section does have same gain that can overdrive the amplifer near clipping points, it can indicate this by going overboard with positive db levels above the 0db reference. That accounts for some gears having a +6db or +12 db above the 0db, indicating a preamp gain of such an amount above the reference value. Some amplifers that are conservatively rated can tolerate a few more input volts above the value that will drive them to rated power. Other's sound terrible even near the 0db mark.
It's also possible that the 0db mark corresponds to 80% or so of the rated power. So that the positive values up to the max will drive the amp to its rated power instead of going above it. That's entirely within the design prerogatives of the manufacturer.