Everybody has to deal with diacritics, be they phoneticians, syntacticians, or politicians, as long as the language involved is one of the majority of languages that uses diacritics. Diacritics are simply little marks put somewhere near a bigger letter which happens to also be useable without the diacritic. For example, the letter usually refers to the sound in English "dog"; whereas <đ> with a diacritic refers to some kind of palatal-ish affricate in some South Slavic languages, a dental fricative in Saami, and [ɗ] in Vietnamese. So diacritics are basically ways of writing speech without inventing a totally new symbol for each sound that isn't found in Latin (at least written Latin, since length in Latin has to be written with a diacritic).
You're really asking 3 questions: the function of diacritics; the logical relationship between phonetics and phonology; plus, you're assuming a specific theory of what phonetics vs. phonology without technically asking whether your characterization is correct (I would say it is not, although it's only yards off, not miles off). I kinda think this question needs to be tightened up.