ZSE Controller described an apparent false MSAW Alert event noting the ERAM software logic operates differently from the Host; surmising the ERAM MSAW is not based upon an aircraft's position but rather its trajectory.

Narrative

Aircraft X was flying from Portland Approach's airspace to the SLE airport. They were filed over UBG..OCAYE..SLE. OCAYE is a fix on an RNAV approach for the airport; but Aircraft X wanted to just do a visual approach. When he was about 10 miles North; I cleared him for the visual. When he descended below 030 the MSAW Alert started flashing. I called the ERAM SMEs over to observe and write up the situation. I pulled up a route line to see what it showed; thinking that ERAM might be basing the MSAW alert off of the aircraft's trajectory as opposed to the aircraft's location. The route was showing a position roughly at the UBG VOR; over 30ish miles North; then down over OCAYE and finally into SLE. At the SME's suggestion I re-routed the aircraft direct to the SLE airport and the MSAW immediately quit flashing. It appears that the MSAW in ERAM is not based on the aircraft's actual location; but rather on where ERAM thinks the aircraft might be. The obvious problem with this is that I don't care if the aircraft's trajectory is going to hit a mountain; I care if the aircraft ITSELF is going to hit a mountain. False alerts like this one are not quite as bad as no alert at all; but obviously false alerts have a safety factor themselves. To my recollection; HOST doesn't work like this. ERAM needs to either update the trajectory to match what the aircraft is doing; presumably not issuing a false MSAW alert; or needs to base MSAW strictly on the aircraft itself; not on the trajectory.