You'll need to blend the colors yourself if you want to incrementally tint it, eg. Color currentColor = tilemap.ColorChannel.GetColor(x,y), then blend it with your color and assign it.
OnTrigger2D wont work, as it is an edge collider, it doesn't have a "volume". We don't plan on changing it to anything else at the moment, the overhead of using different collider types is very very large, especially for larger tilemaps.
There is a much better way to find out if you're inside a tile, just use tilemap.GetTileIdAtPosition - that returns the contents of the tile, and in your case the colliders are rectangular. Try using that over a raycast / trigger - performance will be way way faster than those anyway as its just an array lookup.