The question you gotta ask is: What are you losing by going the full 15? A bit of convenience.
What you gain is that all the metal parts are sanitized even those not in direct contact with the wort. It'll take a couple of minutes for the whole chiller to come up to peak temp and that temp will be lower the farther you get away from the wort. Unless you measure the temperature, you won't know how long to keep it there. In a pessimal set up 15 mins may not even be long enough.
In any case, it is highly unlikely to be a real problem though. However, do you really want to worry for the next 6 weeks to see if that little drop of condensed water that dripped from your chiller is going to cause an infection?