It should be an easy thing to talk about - when a guitar is in tune, that’s it - right? Well, sort of. Certainly, if it sounds right, it is right, but if you use a tuner, think again.
I think that modern day digital tuners serve to reassure us that everything is ok, to give us confidence so that we don’t spend ages twiddling those little knobs. It’s modern technology - it must be accurate! Actually they are just a useable compromise for tuning quickly, certainly not good enough to judge intonation with.
Buy yourself an analogue tuner, one with an actual moving needle on it. Play the note and watch the needle. It does not stop moving for about 4 or 5 seconds. If you listen carefully while you watch, you will notice the pitch of the string changes in step with the needle. The changes are significant, certainly enough for you to query your tuning.
It comes down to this - you need to decide which "part" of the note you are interested in. Let the note ring for a while, then make a choice as to which part of the note you want to tune: the part that you hear at the start or the third second, the fourth etc. etc.
If your style requires the notes to linger, then you may decide to tune to the later part of the note, if you play quick runs, maybe the first part. When you make adjustments for saddle position to get your intonation just right - have a good hard think and watch that needle!