The only way a discount can auto-apply would be if you leave the Discount Code field blank in the discount's settings. When a discount is set up without any Code, it will auto-apply to any order that meets the discount's other conditions (specific item, expiration/use count, and/or min item qty./total). This has always been the case, even with our old Admin. Note the distinction between a Discount Name (which we use to keep track of which discount is which) vs. a Discount Code (which the buyer must enter in their cart to claim the discount).
Nothing has changed in the way discounts work; we only rearranged how the settings appear in the new Admin, to eliminate common pitfalls caused by some unintuitive technicalities -- e.g., in the old Admin, changing an existing Discount Name actually created a new discount under the new Name without removing or altering the original discount under the old Name, and it wasn't clear that item-specific discounts alter the original per-unit price (and thus get multiplied by the item quantity) whereas All Cart Items discounts only apply a single discount to the cart total.