For brass instruments, the pitch is determined by the breath and embouchure. First, learn the embouchure that produces a good tone, then adjust the pitch. If you are playing in a brass-only band, I don't think you need to spend any extra time tuning as long as the sound is clear.
I see many schools that pull out the tuning tube for French horns for a long time. This instrument is designed so that the pitch is tuned with the right hand inside the bell, so if students hold the edge of the bell, the pitch will be higher. If it is too high, first adjust it by putting student's right hand inside the bell.
The position and shape of the right hand are also shown in Method Books, but this also affects the tone, so adjust while listening to the sound. However, please be aware that some elementary school students may find it difficult to reach the inside of the bell with the palm of their right hand.
In addition to the difference in pitch between natural harmonics and equal temperament, brass instruments have some sounds that are difficult to tune due to their structure, which involves stretching the tube to change the pitch. This is a Pitch deviation caused by the combination of pistons, and is basically the same for all brass instruments, so it's a good idea to remember the simple mechanism.