Since the nearest town was rather close, Thufrat didn't really need to ride on Ark's back at all, making that entire discussion quite pointless. Though the town was rather small, they managed to find a rather suitable steed for Thufrat there, before they set off for their journey once more. The steed they had chosen was a type of horse that made use of lightning magic to increase its speed tremendously, and Ark had to use some of his mana to be able to keep up at all.
Naturally, the same could be said for the horse, as well as Ephine. Since Atar didn't really use magic much and had an abnormally strong body, he was able to keep up even without using magic, which helped Ark in getting a perspective of just how strong this little fellow had gotten. The reason Ark was so strong was obviously because of his strong mana, whilst Atar didn't use it at all.