Remember that Rand now has access to Lews Therin's memories, and knows what each Forsaken looks like - in their original bodies.

So he would know if Taim was the actual Demandred.

In LoC it was more a case of Lews Therin seeing something else that made him feel Demandred is a real threat and in close proximity.

I still think it related to some kind of "aura" that Demandred projected over Taim, similar to the weave that Sammael used to send that mindless messenger to Rand, but different in the sense that he could possess Taim part of the time.

When Taim started physically shaking before returning to his normal self, I believe that was Demandred withdrawing when he realised his anger was threatening to reveal too much to Rand.

Something to that effect. Spiritual presence, but not physical presence.