If the service was rendered in 2015, it hits the 2015 deductible and OOP cap. If rendered in 2016, it should go into 2016. If you visited the doc for a procedure in 2015 but the pathology won't be performed until 2016, yes, I'm pretty sure the procedure will hit 2015 and the pathology 2016.
In reality this has nothing to do specifically with an HDHP or HSA. Pretty much any insurance model would work the same way.
"Hey, for every ten dollars, that's another hour that I have to be in the work place. That's an hour of my life. And my life is a very finite thing. I have only 'x' number of hours left before I'm dead. So how do I want to use these hours of my life? Do I want to use them just spending it on more crap and more stuff, or do I want to start getting a handle on it and using my life more intelligently?" -- Joe Dominguez (1938 - 1997)