SAMPA of a language - phones or phonemes?

The 'phonemic touch' of SAMPA is not really a feature of SAMPA but of it's developmental relationship to IPA.

There are two key things to know about IPA:

1. As Colin Fine says, it is always only used approximately. To encode every last fronting of a vowel, devoicing of a consonant, etc. would be prohibitively time consuming. So a phonetician will only transcribe with as much precision as is necessary to illustrate what they're focusing on. Which is why in a dictionary, you will find IPA used purely phonemically, because the phonemes are what matters.

2. Since IPA is really used as an aid to communication among linguists (with some extension to the broader public), it has developed language-specific flavors. For instance, in British English the [æ] is pronounced more like [a] today. But due to local custom (sort of backward compatibility) it is still commonly transcribed as [æ]. Phoneticians know what is going on and are more precise when needed while nobody else really cares because there's no phonemic contrast.

So in a way, IPA itself is used with a 'phonemic touch'. SAMPA is really a straightforward one-to-one mapping of IPA characters to ASCII characters. But because it has many fewer characters to deal with, it didn't make sense to just map the entire IPA to it. So SAMPA was developed for the needs of individual languages. What's more, it's mostly focused on segmental transcriptions and ignored prosody. There are other versions like X-SAMPA and SAMPROSA that try to make it more equivalent to the full IPA. However, even then it will only be used as phonetically or phonemically as IPA itself would be.

You can find more info about the history and use of SAMPA on http://www.phon.ucl.ac.uk/home/sampa/.