Hmmm...that's what horses do, whether you sit on him or not. If it happens while they are turned out, it looks like a chain reaction: one horse runs, a second later the entire farm is running. To the horse, if a horse is running, it must have a reason for doing so.
A few weeks ago, I took a lesson horse on a cool-down walk around the farm. We walked past a pasture, and the three horses, seeing us, were hauling a**. My horse thought there is something concerning going on and also sped up. Nothing extreme - just a speedy trot which I let him have to the edge of that pasture, but still... Let me reiterate: That was an experienced show-, and current lesson horse. If I had sat on a greenie, I'd really have gone for a ride!
I once cantered along the tree line of a field, when suddenly a deer jumped out in front of us and turned into our direction of travel. My horse turned on the afterburner and -- followed the deer.
My guess is, your horse will always get somewhat excited when he sees other horses running. It'll just become less severe as he gets older and more experienced.