Transposing that reads like it was written in the new key
Moving every note up a minor third is the easy part. What makes a transposed part readable is the spelling: in E flat, the note between D and E is E flat, not D sharp. Here the key signature moves with the music, and every note is spelled from it, the way it would be if the piece had been written in that key.
Some keys have two names, F sharp major and G flat major for one. The transposer picks the one with fewer sharps or flats, staying on the side the piece started on, and lets you switch, since that decides every accidental on the page.
For a B flat clarinet or trumpet, an E flat alto sax or an F horn, choose the instrument and the part comes out at the pitch it reads at. To move a song to a singer's range, pick the key, then go up or down the other way, or an octave, until the notes sit right.
From a PDF, the notes are read from the page first. It reads PDFs exported from notation software (MuseScore, Sibelius, Finale, Dorico, LilyPond, Guitar Pro), where every note is a symbol in the file. A scan or a photo of paper is a picture, and it says so instead of guessing. The page shows the transposed score before you save it, so you can check it.
The file is read in your browser and never uploaded: there is no server on the other end that sees it.