Specifically for set a trap, but could apply elsewhere as well.

Logically it makes sense to me that the quarter square interlocking sections should only count for the tile that contain most of the squares but i heard someone say that even those interlocking areas count as being on both tiles.

I couldn't find any rules defining "map tile" in any of the rule books and I just wanted to know if there has been an official ruling on this or not.

It must be obvious if it isn't defined somewhere, because mission rules allow deployment to named tiles.

My definition of a tile would be all of the spaces on a tile.

See Interior Spaces.

That still doesn't really answer the question of the squares overlapping a jigsaw edge. Are they part of 1 tile or 2?

Graphical details (ends of walls extending beyond the corners of spaces) do not determine line of sight rules.

Mechanical details do not determine whether a space is interior or exterior. (Interior Spaces in RRG.)

So, it can be safely assumed the locking fingers that encroach the space on a different tile are not considered to be part of a space that belongs to this tile.

That still doesn't really answer the question of the squares overlapping a jigsaw edge. Are they part of 1 tile or 2?

I tend to assume that the interlocking parts of a tile are a flat line when calculating which tile a figure is stood on. The only reason they aren't flat is so that you don't accidentally nudge the map into pieces all the time.

A "map tile" is quite literally, a single piece of cardboard, with a tile number on it.

If you were to remove the protruding "puzzle" piece and insert that into the gap in the piece next to it, you would have a perfect grid with no "overlap". There are many references to what a tile is in the book, which I will not list here. Suffice to say that setup specifically defines "map tiles", each with a tile number on it.

The "overlap" merely "completes" a tile for stability.

Below, you have two tiles, 19A and 23A. 19A consists of a 6x6 tile, and 23A consists of a 4x4 tile.

Separated they are still the same number of squares on a tile. Still 6x6 and 4x4, respectively.

If you could give a book reference for this I would love to have it.

Like I've said this is the way I've always understood it to be but have heard others argue that they could trigger Set A Trap played on 19A because I had a figure in the doorway on 23A and it seemed wrong but I have been unable to find any evidence other than feeling. I just want to be prepared with something solid to use if it comes up again.

Just place the figure so that it does not fall on top of the 'finger'. They can not argue it being on that tile then.

(The correction question for confirmation is to ask "Does on the tile refer to the spaces on the tile or any part of the physical tile?")