I'm so glad smartphones and this type of thing wasn't around when I was in my mid/late teens! I was given a reasonable amount of independence at around 15/16 and while I wouldn't give chapter and verse, there WAS a generally mutual respectful dialogue where I'd tell my folks where/when/who with and when I planned to be back. Beyond that, there was trust. That communication continued and while over 18 I didn't have to say anything really, I did keep that mutually respectful communication going - at the very least giving some indiction of when I planned to be home (ie before/after midnight) out of courtesy.
But had there been this tracking lark then, I would have resisted it with everything I had - not because I was "up to something" but on principle. I never really did anything particularly controversial, but this "tracking people" tech gives me the creeps and would've changed the whole dynamic of my relationship with my folks.
Had it been "enforced" (a la "no tracker, no phone" or similar) then three things would've happened: 1) I'd have saved up every penny I got to get myself another private phone with the "tracked" phone becoming nothing more than a piece of plastic I would strategically take/put wherever I wanted to be "located" while I was actually no where near. 2) I'd have turned it around and driven my mum INSANE with it - constantly messaging and asking why she was in X place AND given a running commentary on where I was (including every time I went to the loo - EVERYTHING) - to where it would be stupidly boring for her - I'd comment on her every move too and if she complained I'd have responded with "but why is it a problem if you're not up to anything... I'm just checking you're safe. And you wanted to know my every move so I'm just giving you want you wanted". And finally 3) - and this is the most important one - that positive communication I had with my folks - would've been gone. I'd have made it a point to tell them bugger all - or at least fed them BS. I'd have lost that mutual respect with them and I'd have gone all out to make sure they had no idea where I was. Safer? Not so much.
I don't get the issue re the 6am jogging - it's not the middle of the night! I could understand the concern a bit more in the winter when it's pitch black and horrible then, but at the moment? I don't get the worry - I'm up at that time frequently and there are loads of people jogging at that time. It's a very common time for keen joggers to get out - either to get a run in before work or before it gets too warm/busy etc.... joggers and dog-walkers are often to be found at 6am round here (and in other places I've lived too).
I get you want her to be safe (although if I'm honest, I think you want to track her for more than just "keeping her safe"), but be careful it doesn't backfire.