You are working with a violin. It has four strings tuned in perfect fifths. Intonation on a violin, which has no frets, is something that you produce with your fingers, not with an electronic measuring device like your tuner. You can produce any kind of intonation or temperament on a violin that you can train your ears and fingers to recognize. You are not limited to twelve exact pitches in an octave. You can slur up or down by any amount, to produce vibrato, or any kind of microtonality.
Various different systems of intonation or temperament, like those found on your electronic tuner, chiefly apply to tuning keyboard instruments like the piano or harpsichord.
Electronic tuners that provide various schemes of intonation are used for "early music", "historically-informed performance" and the like, to tune replicas of "historical" instruments to play music that was composed in the years before the modern system of 12-tone equal temperament came into popularity. Basically that's anything before the beginning of the 20th century, but it applies particularly to any music written before the beginning of the 19th century.
Bach, Handel and Vivaldi did not use modern 12-tone equal temperament like on the modern piano. Today, many people play music written by these composers on modern instruments in 12-tone equal temperament. However, there are some musicians who practice "early music" and "historically-informed performance", and they perform these pieces by these composers using the earlier tuning systems that these composers actually used when they composed the music.
I work for a Baroque chamber orchestra that plays replicas of instruments from circa 1640 to 1790, and they tune to A=415, a half-step lower than the modern system of A=440. They tune their harpsichord and organ to a fractional-comma mean-tone temperament system that only works well in certain keys, and all the other instruments (such as the Baroque violin, viola, cello, viola da gamba, and bass violone) play in tune with the harpsichord or organ. An electronic tuner with alternate historical temperaments is something that this group might conceivably use, although our harpsichordist is so experienced that he can tune his harpsichord to any of the commonly-used historical temperaments entirely by ear, without using any electronics. He starts with a single pitch from one tuning fork and listens carefully and counts the beats of slightly out-of-phase intervals as he tunes the harpsichord.