If events happen that Michael doesn’t know about, does that mean that he isn’t dreaming?

In the 2012 TV show Awake, Detective Michael Britten switches between living in two realities, one in which his son is alive and one in which his wife is alive, with the strong implication that the realities are related to dreaming. Every episode begins with the following intercut exchange with his two therapists from the two realities (a longer version appeared in the first episode).

Michael Britten: It all feels completely real to me.

Dr. Lee: Meaning you can't tell whether you're awake or asleep at this very moment?

Dr. Evans: Well I can assure you, Detective Britten, this is not a dream.

Michael Britten: That's exactly what the other shrink said.

However, we see over the course of the series that a number of events happen without Michael being present, and in situations he couldn’t possibly have known about. For instance:

• In the Red Reality, Britten’s wife Hannah has a private conversation with one of Rex’s friends about the motorcycle parts she’s been shipped, which Britten doesn’t know about yet. (The Little Guy)
• In the Green Reality, Britten’s son Rex has a private conversation with his girlfriend in his room, despite Britten never having met her. (That's Not my Penguin)
• The people behind the conspiracy to frame Britten, in both realities, are shown talking to each other in private long before Britten knows who they are. (e.g. The Little Guy)

This doesn’t seem to be a case of Britten knowing about the events subconsciously or that he is having an out of body experience and is witnessing them; he has no way of knowing that these events are transpiring and, when he finds out about them, his reaction shows that he never suspected that they were occurring in the first place. Also in all of these situations, Britten is awake and presumably having his own off-screen experiences.

The only real exception to this is in the final episode (Turtles All the Way Down) where a private exchange between the conspirators is shown, then Britten is later able to witness those private events as an unseen observer (with the help of his partner dressed as a penguin, which is as bizarre as it sounds).

It’s clear that Britten is experiencing two realities. But does the fact that things happen without his knowledge indicate that he is not dreaming?