>Yancy will automatically call the player on any one of fifteen specific spots. They can only be triggered once. Each spot is only located at one specific tile.
Nimbasa City (behind the Battle Institute)
Driftveil City (on top of the northern hill, below the Worker guarding the Clay Tunnel entrance)
Lentimas Town (on the path behind the northern house towards the hill with the Fire Stone)
Mistralton City (on the southern half of the runway, in the center of the lane)
Undella Town (southwest corner, up the stairs and between the two boulders)
Lacunosa Town (under the bridge in the center of town)
Route 5 (on the other side of the southern fence, towards the Hyper Potion)
Route 6 (just above the two shortcut ledges on the south end of the route, east side of the stream)
Route 7 (on the path between the Pokémon Breeder and the southern house)
Route 9 (at the left of Shopping Mall Nine, near the L-shaped bush)
Route 11 (in front of the truck, between it and the stream)
Route 12 (on the highest hill, lower-leftmost square)
Route 13 (on the south beach, between the running Ace Trainer and the Fisherman on a sandy corner by the water's edge)
Route 14 (towards the Abundant Shrine, on top of the waterfall with a small square of land on the right, west of the Backpacker)
Route 16 (west side of the route, south of the Depot Agent and north of the male Cyclist, middle of the road)
According to Bulbapedia, Yancy/Curtis can call you at those places at specific tiles. You can also call Yancy/Curtis anywhere from those areas, but they will only call you if you stand in those specific tiles.
These images should be in the same order as the list above.
Hope this helps!
Sources:This and this.