"Sitting on the tempo" is an expression often used by musicians meaning that you take your time with a steady tempo but without dragging.
It allows you to play in a relaxed manner and improves your rhythmical precision. I also find that I have more endurance when I take my time because being relaxed helps me to take more air which sends more oxygen in my blood and helps me playing a bit longer.
Practice with metronome to make sure you don't rush. We don't always notice that we rush when we're used to play in some way. Sometimes we make our life harder than it should be!
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.