It all comes down to knowing the intonation tendencies of your specific instrument or instruments. I have a Calicchio flugelhorn that has a rather sharp tuning C (concert Bb). If I pull the tuning pipe out to get the C in tune, everything else is flat.
I spent a lot of time in grade school and junior high honking at the Conn Strobo-tuner, getting the dials to settle down to the band director's satisfaction. Almost 40 years later my philosophy is, "don't tune, just play in tune." I know how much tuning-slide pull my daily players usually need, and I'll generally play a note in response to the obligatory "tuning note" and make of show of fiddling with my tuning slide while not moving it.
Unless the band is playing with a real piano, in which case tuning probably matters, or if the venue is particularly hot or cold.
The most important things are having "big ears" and just playing in tune.