Do you pre-soak with 38C water to warm the tank up? If not it will cause an immediate drop in temperature which might lead to this result.
I've done a 3-film batch in a Paterson tank with the Adox E-6 kit, so far I'm impressed with it, but want to see its longevity.
Yes, I pre-soak for 4-5 mins (they recommend 2mins). The water bath is around 40deg. But the tank is submerged in the water bath to a bit above halfway up, and the 12 inversions (once a minute) take around 20s, so the tank spends only 2/3 of the time in the water bath, and then it's submerged only to about halfway up. the room temperature is typically 18-22deg (winter/summer). I'm pretty sure that the 1st Dev temperature decreases from the initial value (of around 38.5deg), and that might well explain why I seem to need 7mins30sec instead of the stated 6mins15sec. I know I should do some measurements and experimentation, but I have a routine that "works".
I've processed about 150 Provia in the past 5 years using the Tetenal/Bellini and now Adox E6 kits, and I've always had to give the longer 1st Dev time for all three kits. That does not worry me: I just do
exactly the same process every time, adjusting the 1st Dev time for pushing the speed (or not) and as I develop more films in the same solution.
I make 3-4 short photo trips a year around Europe, taking 5-8 rolls of (mainly, 90%) 120 film, so I use the 1 litre kit in one extended processing session over a few days. I have never kept the diluted and partly used solutions for more than 3-4 days, and rarely kept the opened half-empty stock solutions for longer than 2-3 months (using Protectan or equivalent). (I used to buy the Tetenal kit in the 2.5 litre version.) So I don't really know about the longevity and would be interested to hear your experience (later this year?).
By the way, Adox recommend an extra 2mins in the 1st Dev to push by one stop, so that gives you an idea of the tolerance on the 1st Dev time. People make a big issue of saying the 1st Dev time should be exact, but a "sloppiness" of 30sec is the equivalent of 1/4 of a stop on exposure ... hardly noticeable by most people including myself. I'm not recommending anyone be sloppy in the timing but I feel it's best to focus your energy on getting the temperature "correct", or at least the same temperature for every film you process.
My photos are medium format stereo using cameras like the Sputnik and TL-120, and the stereo transparencies are viewed in an optical viewer (like a very large ViewMaster).