Does points of interest change from byte to byte?

I launched a few days ago a template attack, I try to find some bytes from my 16 bytes of the secret key. When I try to calculate the points of interests, I found that I have a different values for each byte .

For example:

Byte[0] =[3836, 3829, 3842, 3822, 3848, 6977] Byte[1] =[4713, 4719, 4706, 4725, 4699, 4692]

Absolutely, yes! What this means is that the different bytes of the state are being processed at different points in time, which makes sense - software encryption can’t do 16 operations at once.

Thank you very much for your answer,
So, according to your answer, I must have 16 different intervals of Points of interests and 16 different trace of sum difference (tempSumDiff), trace for each byte.