Yes. You are probably taking it too literally.
I don’t know much about Karate or any other Japanese martial system. But in my experience with various Chinese martial arts schools there’s a similar concept that my current teacher translates as deflect-attack.
The idea is that you should not see deflection (or blocking) and attack (be it a punch, or a kick or a throw as two unconnected moves that just happen to follow each other in a sequence.
In the arts I am practicing (and I have a strong suspicion that in all martial art practices beyond beginner level), this means that when blocking or deflecting the opponent’s attack, you should also lay the foundation of your counter. The best deflection is the one that not only protects me from your punch, it also lines up my counter punch and disrupts your follow up.
In that sense, deflection (or blocking) is part of the same move that becomes an attack or a throw or whatever is going to be your countermove. And thinking of these things as one continuous move regardless of its final shape is the mental model one should assume when free-playing. One should flow right into the other that should flow seamlessly into the next move and so on and so on.