The phase difference will depend on the time of day that the Arduino was started..
No problem with that - I want to see just the drift, the absolute value is not important at this stage.
Interestingly, after several starts (random against RTC) the number I get after a while (I am sampling the diff in a loop every aprox. 1.2secs) is always around -0.6 (the aver_dt is still noisy, but clearly around -0.6). So there must be some hidden "principle" in it. Trying to understand that..
What I would do is connect the 1 PPS signal from your RTC to an interrupt pin
Still looking for a way how to do it with "RTC's seconds" and some math..