The IFD is providing all of the deviation data to the Aspen via ARINC 429 (digital) and the Aspen then sends that digital data to the ACU, which processes the information and outputs the analog equivalent to the autopilot.
The way the Aspen does this is dependent upon what mode is selected on the Aspen. For instance, in GPSS the Aspen listens for ARINC429 label 121 (roll steering). The Aspen then takes that roll steering deviation information, and via the ACU drives the HDG input on the STEC. For roll steering/HDG inputs, the scaling is typically around 550 millivolts per degree.
During an LPV approach, the Aspen will take the cross-track error from the GPS, and via the ACU, turn that into analog Main Left/ Right inputs to the autopilot (which the autopilot sees as an ILS input). The scaling here is much tighter for obvious reasons. 150 millivolts = full scale deflection on the CDI.
Based on the above numbers, you can see that while in GPSS, your +/- within 1 degree (equivalent) of heading data could easily be up to 3.5 times "wider" than even full scale deflection when driven via Nav mode. By leaving the GPSS engaged we all but eliminate the "precision" of an LPV.
Another way to look at it, is that the closer you get to the runway, the tighter (more accurate) full scale deflection becomes (but not in GPSS). So flying enroute, full scale deflection on the CDI in GPSS mode may be up to 2 NM. On approach, full scale deflection may be .3 NM or less. GPSS does not account for this "tightening" because what is sufficient deviation to produce results during enroute will not be sufficient for quick course correction on or near approach.
Because of this, we recommend as standard practice when established and approaching the FAF switching off GPSS, select GPS1 as the Nav source on the Aspen, and put the AP in NAV/APR mode. This will establish proper scaling to maintain accuracy as the lateral deviations get tighter.