One way I do a similar thing is I make a grid of sprites that are camera points and I ScrollTo the camera points depending on which one is closest to the player. This way I completely control the camera bounds.
Not sure what your game looks like, would probably help if you made a project mockup of what you are trying to do. But it seems like AllanR had the answer, you just need to dynamically pick which tiles are relevant as your min/max depending where the viewport is in your layout. Some sort of nearest calculation should do it where you are always changing those values depending where the player is in the layout.
Assuming you are doing and abrupt scrollTo it should work without any overlap.. but if you are using some sort of lerp for your camera, there will be bleed since if you suddenly change the min/max and are currently out of the bounds, it will then need to lerp to the new max/min and you will see it do so.