I am not completely familiar with the Zero TA, but I have 1st Gen Duo Omegas which are 107 dB.
I do not believe that the TAs are self amplified ( like the XD series ), what amplifier are you using?
It could be a matter of making a gain adjustment somewhere in the signal path.
The DS may exhibit a very tiny amount of self noise on the higher output, but engaging the -20dB attenuator will completely remove that noise, so long as your amp still has enough gain.
If you can not hear the hiss at your listening position I would not be to concerned.
I know with my horns, placing your ear up to the horn is like holding a conch shell against your ear at the beach, you seem to hear all sorts of amplified ambient noise that is not really coming from the horn.
How are you connecting the sub section of the TA, separate line level or connecting to the speaker level?
Currently I run DS SR directly via 30 foot XLR to a Decware ZBIT ( to convert to rca ) to connect to a Decware SE84UFO25 amp for my DUOs.
Even with extensive power conditioning, very low level hiss and hum will come and go, but is never audible at my listening position.
Except when a hair dryer is used in the bathroom, the noise that is thrown back onto the line and or into the air is very evident through my horns!