He does need to calm down as well as Ignis. This was a rollercoaster of emotions and stress- both on body and brain and they need a break. Because if Ignis knows Noct the way he thinks he does, Noct won't calm down until he reaches and saves Shiro.

But he needs to collect himself before he does anything or his mind might melt. Those memories felt... real. Ignis can still feel shocks from both Noct's and his memory.

"No," Ignis shakes his head. "You found me and got me out." He frowns, fingers digging slightly into Noct's clothes. "Don't worry. We'll look for both of them as soon as we take a break. Alright?"