Strange can recognize the spell. As soon as Axii hits, he can sense the magic and piece out that it's Lambert's magic and the nature of the spell itself. He doesn't need to do this. This is just the magic speaking, just the magic telling him to do something. He doesn't want (or need) to do this himself.

But it sounds like such a good idea. Of course he wants to run around the ring, why wouldn't he? Yes it's the magic, but if the magic is telling him to do something fun, then might as well listen. There's a moment of hesitation before Strange does decide to run around the ring, though he stops halfway through. The internal battle of Lambert's spell vs. Strange's mind might have taken longer than expected, but Strange's mind came out on top eventually.

"You can only command someone to do a certain action, correct?" he asks, trying to push back the confusion he's still feeling. "The spell can't change one's personality?"