Huge delay changes can change the seconds you land in the game, so every once in a while, you may find you need to adjust the DS minutes for this reason. But otherwise, if you land within a delay range +/-10 of your target, you should remain on the same DS starting minute once you've adjusted properly to land on the correct seconds.
Example:
My target time is 15:05:16. My wanted seconds on RNG Reporter is listed as 16. My wanted seconds on PikaTimer is listed as 16. My calibrated seconds remains the same as always. In my case, it's 16.
I set my DS to 15:04.
I land on an adjacent delay on the wrong seconds. The adjacent delay has given me a +50 when I add it to Pikatimer in other delay. This first time, I do not fix my DS minutes. I use the adjacent delay in other delay on Pikatimer and try again, just to test what second I will land on with this big jump of +50.
Next time I try to get into the game, I discover I land in the game closer to my target delay, but I'm now another second too early. That's two seconds off.
Based on my results, I set my DS clock to 15:06, two minutes later, in order to arrive a on my target seconds. I do not change the wanted seconds on Pikatimer. I don't touch the calibrated seconds either, because my first result came from using those settings. Changing them would ruin my next attempt. So I try again with the new minute on the DS (15:06). I land on the right seconds this time.
Whenever you adjust the delays because of an adjacent, you risk going up or down a second when landing in the game. Just adjust the DS minute down or up in response.