Then in the briefing room Kirks says to him "You have a theory about why our sensors didn't pick up the Romulan ships?" (as best as I can recall) and then Spock tells him he believes the Romulans have developed a cloaking device....etc. They're didn't appear to be any wink/nods going on. It was as if they weren't aware of this ability at all before then.
Uhhhhhhhh... That's how pretending works. You're not supposed to give obvious winks and nods, because that's a lousy way to keep a secret.
Why bring up the cloaking device they are supposed to steal at all? If you want to throw everyone off the scent of what the plan was, why would you bring up the very thing you hope to steal in the first place?
Because the Romulan ships just appeared out of nowhere in front of the crew!!!!!!! Obviously they needed an explanation for that.
It just seemed the wording of the dialogue made it seem like they were unaware of the Romulans having a cloaking device at all.
Asked and answered.