I think Dr. Junkin’s tempos here are quite measured and in line with how Williams himself conducts the piece. Contrast that to the piece from Hook they also have up on YT which is extremely rushed and almost manic, particularly in the opening section.

Personally as someone who only knows this piece by listening this feels pretty similar to how I hear the original composition played. I'm not sure if the Lavender arrangement has a different tempo from the Williams original but this sounds right to me.

I’ve worked with John Williams and can vouch for my comments. Jerry is a great musician, but the musical choices can be refined. The band still does well for the most part. The decisions on the podium can help ground your musicians. It takes years to master it. No one is perfect. My guess is that adrenaline has something to do with it. Jerry tends to do things faster than everyone. Faster, higher, or louder doesn’t always mean better. This piece has a lot of parts that connect with one another so transitions and tempo choices are crucial for the band to play it seamless.