The delay is presumably for theft prevention; and also to prevent fire alarms from going off when someone simply and honestly mistakes a fire exit for a real exit in an non-emergency sense.
The building safety and fire codes that allow such a delay will be very localized at the city/county/state level; you may be better off asking at that Costco, asking Costco at the corporate level, and the local fire department; all should be very up front for the rationale behind the delays and with your safety concerns. Edit: see user6726's answer for some relevant local codes.
Buildings that are open to the public (and in some cases, private buildings) are subject to regular fire code and building inspections, depending on local/state/federal laws. The inspections cover fire exits, alarms, sprinklers, occupancy ratings and structural inspections, and more. These same inspections can take place when a building is sold or when a building permit is issued for work. And these inspections can sometimes take place at random, too, depending on local codes. So if the delay mechanism on the door is illegal, it will be spotted at some point.
Costco as a corporation will have a building division with specific engineers tasked with building safety and liability. I'm sure Costco has done their due diligence for each store location and the relevant fire codes dealing with delay devices to help prevent "product leakage"; the liability - both real and imagined in terms of marketing and PR - is too great to make a mistake.
Presumably there are research metrics that allow the calculations for a reasonable time span of the delay allowed for the opening of exit doors. Building safety and fire codes codes will take into account the number of exits in a building, where those exits exist (ground floor, upper floors with exterior stairs), the maximum occupancy of a building, as well as other factors such as seismic threats and the survivability of a structure in an earthquake, the speed at which a fire can expand and when smoke may fill a structure, and more.
15 seconds isn't that much time; think of the time you might stand still and look around after you first heard a fire alarm. I'd say that's easily 15 seconds. But 15 seconds is a long time for someone to stand and wait at a door if they are stealing. To be clear, I'd be a bit curious and maybe worried if I saw that sign; and esp. if I saw a fire door locked/chained closed, which would be highly illegal and outlawed by code. But I can see a reason for such a 15 second delay.