Creation Magick is the process of transforming Aether into matter, shaped only by the will of the user. There's no violation of physical principles because we know from in game lore that all things are made up of aether. In a sense it parallels our own physical world where all matter is energy when you look at it from a quantum scale, hence why mass can be turned into energy and vice versa (laws of thermodynamics). Since all things in FFXIV are made up of (not just contain) aether, its a simple matter for an Amaurotine to use their own internal aether stores to create matter from nothing. The matter comes from their own bodies, which again has vast stores of aether.

Now, crafting is the act of using aether stored in an elemental crystal to power/aid your synthesis. The heat provided to melt the iron ingots or boil the water or liquify gold, etc, the wind to help shear the fabric, the earth to add pressure or force to your hammer, ice to cool and condense reagents and reactions, lightning to carve, split, or divide objects, you get the picture. The mass is provided in the recipe, the crystals are catalysts of energy to aid the proccess, but we are still shaping items based on knowledge and using our own tools to craft. It's not like FFXI "synthesis" which was a form of creation magic. In FFXI you throw ingredients and materials into the air, activate a relevant elemental crystal, and the think of a mental image of the finished product, and shortly after the finished product poofs into existence. In that world, your "synthesis skill" for each craft was a measure of how focused your mental images of the finished product were and not so much your actual skills with a doming hammer or carpenter's saw are like in XIV.