In my opinion, chasing a horse is never a good thing. While free lunging, I do as you suggested and will ask for a walk, trot, and canter, but will avoid pushing them into anything faster unless they pick it up themselves or are really misbehaving. You also mentioned this being a rescue, so I assume these ponies are out of shape, in which case I wouldn't be pushing them that hard. (I could be wrong though, and as EponaLynn suggested, they could have had reason for pushing him that hard. 5-10 minutes is not extremely long for a horse to be running either).