If there is one thing Kurama is very good at, it's composing himself in the blink of an eye. Prioritizing getting them separated makes the most sense for many reasons - assuring that it's even possible being high among them. It was also as much a demonstration to Hiei that they'd had no real choice, whether the message sinks in or not is another matter.

Why it makes any difference to the fire apparition in the first place, a third and separate matter.

They probably would have detached already if Hiei hadn't showed up. Another shining example of how this universe seemed to be inconvenient with intent rather than by coincidence. Kurama slips both hands into his pockets once they're released, letting Kuwabara take on the confrontation with Hiei. It came far more naturally to the two of them, anyway.

“The tunnel is merely childish entertainment. Nothing to get worked up over. If you'd like, we could go through together and you can see for yourself.”

Does he expect to taken up on that offer? No. Does he expect it to possibly distract or embarrass Hiei enough to derail is current irritation? Maybe.