I was also stumped here, but I finally figured it out. The mimics, hat, and coin all have to be placed within the blue zone on the main screen surrounding the X.
Now, on the sub-screen you connect the line tiles, BUT in addition to those connecting lines, there are five extra "symbols" on those tiles: each of the four corner segments of a circle, and a short horizontal line. Those circle segments dictate what corner of the blue field you should place the adjacent item, while the horizontal line indicates the bottom-center of the blue zone since the top-center is already occupied by the X.
For example, on the sub-screen the coin symbol is adjacent to a map tile that has the bottom-right segment of a circle. Therefore, the coin goes into the bottom-right corner of the blue zone on the main screen.
The hidden images you find with the torch are sort of a red-herring since they are actually clues to the next puzzle.
If the dev happens to read this, I think that making the circle segments and horizontal line markings a different color from the connections would add a little extra needed clarity to the puzzle. For a long time I thought I was somehow expected to "follow" the connecting lines to find where to place the item or that they were somehow related to the full layout of the main screen. I had to put down the game for a couple days ultimately. Once I had finally solved it I was able to complete the rest of the puzzles in this trial demo without nearly as much struggle.