I think you might be confusing tile size with sprite size.
All my tilesets are based on a 16x16 pixel framework. Some objects (or sprites) occupy more than one tile.
My doors are 2 tiles wide and 2 to 3 tiles high. My trees are between 3 and 5 tiles wide and up to 6 tiles tall, but the tiles are always 16x16.
Breakable Pots (which is not this asset you are commenting on, by the way) includes an animation that necessarily exceedes one tile, but also includes pot shard particles at much smaller than 16x16 so you can make your own animation.
Things like interactive chests and breakable pots should be game objects/sprites, not tiles (it's worth noting that in neither of those other assets, do I describe them as tilesets or 16x16). Unless it's a stylistic choice to have everything occupy only 16x16, I would urge you to account for certain elements being bigger than that.