Does the item being transmitted need to be in the smaller circle on the receiver coil?

No, the item does not have to be in that small circle; However, it is the best place to put something.
This small circle denotes both the start of and where the two coils overlap that creates the tesla coil beneath.
Additional items on the coil should follow the larger circle that touches the smallest circle, so that you are essentially putting the items along the perimeter of the coil.
The last place one would use is the center.

For more details, please check this link:
https://www.facebook.com/groups/spooky2scalar/posts/976300792943479/