Basic set draw stacks
In a normal game of Rivals, there are 4 draw stacks that do not belong to either player. In a tournament game (rules), each player has their own 4 piles containing the cards they most want to play with. In the version of Rivals I could find, no card says "from your draw stack" unless it also explicitly references tournament mode - for example, the text of Library is 


  When you build the Library, you may immediately choose a card from a draw stack (Tournament: from your own stack.)


I know there are some differences between this version and the older one you are presumably playing, but I'd guess that references to "your draw stack" just mean any draw stack outside of tournament mode, and that you might be able to find a fixed wording of your card by looking it up in the back of the linked updated rulebook.