"He is." Having absolutely zero knowledge that Tyki's involved with the Heart business in the first place, Strange is just taking this as nosiness and curiosity. As for Eruka...

"Stay near a reflection. I should be back in five minutes or so." And without even waiting for Tyki to say 'okay, I understand', Strange vanishes from the reflection. Assuming that Tyki doesn't move or drop his hand mirror, Strange reappears in less than five minutes.

"Bad news, she's still imprisoned. Good news, there aren't any honorables or architects near her. I don't know the exact location, but I got a fairly good view of the area around her prism."