Inventory Sync Shopify Apps

Quick question, of i wanted to use SPOD, Printify, printful and then use customcat and teelaunch for custom items, how does it work on terms of allocating the job, like if i have all the same products in different stores how does it decide who is going to fulfill it

I just want something that tracks my supplies that I use to make my products. Example: I make custom hats. so I want to track all my red hats across multiple Design options. So if I sell one design then it updates my other products.