There are two types of personal stores:
1. Personal stores set up on Eden (like the ones listed here
2. Personal stores that are separate websites (like this one
If you are shopping in a personal store on Eden (type #1), you have to be linked to the store with an affiliate link in order for the affiliate to earn commission from your purchase.
If you are shopping in an Eden personal store (type #2) on its own website, anything you purchase there will give the commission to the affiliate. No special links are needed because the store itself is coded to give commission to the specific affiliate.