He should appear in the museum or the lab (to the left) after you have watched all of the videos in the museum.
After Mews leaves your room, drink the water and go downstairs, to the museum on the first floor (right). Watch the 5 videos and then Mews will arrive and you can begin hunting for the cryptids in his helicopter.
The Cryptids Museum is on the first floor of the Mews mansion, to the right.
After you watch all 5 videos in the Cryptids Museum, Mews will return and give you some more instructions. Then you can fly off to locations in the helicopter.
Go to the museum (first floor right) and watch all 5 of the cryptids videos (at least part of each one).
After Mews leaves the room, drink the rest of the water from the glass, then follow him down. Go to the room on the right on the first floor, which is the Cryptids Museum. Watch all 5 videos and Mews will appear at the Lab (to your left).
The heliport at Mews' house is out the door, then to your right. You cannot use the helicopter until you have reviewed all of the videos on cryptids and spoken to Mews.
When you come downstairs in the Mews mansion, and enter the museum at the right, your character will suggest watching the 5 videos on the cryptids. So you have to do that before Mews will appear again.
After Mews leaves your room, drink the water and come downstairs to the museum and lab (first floor right). Watch at least part of all 5 videos, then Mews will arrive.
Review the 5 videos in the museum, and Mews will appear to give you further instructions.
When you have reviewed all 5 videos in the museum, Mews will arrive, show you the lab, and ask you to hunt down the cryptids.
He appears only after you have watched all of the videos in the room (you don't have to watch them all the way through).
It is one of the locations on the helicopter GPS system on Cryptids Island. Once you are rescued by Mews, review the videos and you can go in search of the four cryptids.