With this and tiled - I really don't understand how you hook them into your game without a bunch of code managing the boundary between level editor and real code.
I think you just load the generated file into the game. One part I don't know is how to handle entities. Each game has its own entites and maybe even completely different treatment (architecture) of entites. I'm not sure how flexible they are.
I'm building a simple 2d RPG that is a Ultima spin off and a map editor. In my game I could put different components into entities (not ecs but more oldschooled way) and call each component's update(). Since I'm building my own editor, it's a lot easy to integrate all those into it. For example I could even have a dedicated entity tab that designers can enter some values. I wonder how tiled treat this kind of questions. I browsed through the manual and didn't see anything related so I think it's a pure map editor.
Many Haxe game engines do indeed provide a shim layer which converts things like objects, pathing, behaviours, and triggers from the level engine's output into game logic.