More experienced ninja have shown to have an increased spacial awareness as well as combat awareness. You can see this in various fights throughout the series.
In the first fight with Uchiha Itachi, Kakashi showed that he was able to create a water clone in a split second designed to take potentially lethal damage.
Throughout the series, clones are used as decoys just as much as they are used to mitigate damage done to the user. Obviously the user in these cases know exactly who is the clone and who is the user.
It would make sense then, that young and inexperienced Naruto with a new clone technique (which isn't that much different than other cloning techniques) would not have the experience or spacial awareness to perceive the differences. However a Naruto that has used the technique hundreds if not thousands of times, as well as having participated in numerous fights, would be able to tell right away.
Now exactly how he can tell is mostly speculation, but there are several key points:
- when making the clones, he can choose where the clones appear.
- One could notice that they were not where they used to be prior to the technique.
- One could also notice that they have "appeared" as a specific piece within a specific strategy.
- The consciousness of the clones would see an immediate shift (a pop?) from where he was to where they appear.
- This could also be extended to immediately recognizing one's self as a clone based on "feeling" the shift from using the technique to the clone appearing.
- One could speculate that the user might even "feel" a shift in the molded chakra from when the user is performing the technique to when the clone appears.