One of Remus' strengths was his ability to remain calm in just about any given situation no matter how dire. The only exception was when he sort of flew off the handle upon hearing about the deaths of his friends and Sirius' subsequent arrest. That had been a moment of sheer panic and outrage. But otherwise, he generally and genuinely had a very calm, rational disposition. That was ever so true now, even when he'd been faced with some big cat who then turned into his best friend's younger brother very unexpectedly.
Of course, he had to tell him not to say anything. That left Remus with a heavy amount of conflict. He didn't have secrets from Sirius about anything. Well. Anything except for The Thing. That wasn't really a secret though. They both knew about it -- at least, they did in his time -- they just left it as The Thing. It wasn't he same as this, was what he was rationalizing to himself in those few seconds of silence.
Remus understood the importance of secrets. Hell, he'd been harboring a huge one given what he truly was. He'd also been keeping the fact that his friends had become unregistered Animagii for him a secret for years. "I generally don't keep secrets from your brother about anything," he said. "But I respect that this is not my secret to tell. Might I ask why you don't wish him to know? Or does he know, but no one else?"