OK. I think I was right. Tsukagami Sentarou can't see the dog because he IS the dog. He thinks the dog is just a spell that has no in-between state between two actions. But that's because he's the actual vessel for the dog. However, Haruki can see the dog because when Sentarou is doing a long-range attack using the dog, the dog temporarily exits Sentarou's body and becomes visible to those with talent (or the right soul).
Also, everyone was tricked by the previous Tsukagami. The dog can be directed at anyone its master KNOWS (like when Haruki directed it towards the pedo). The target object is just a replacement for targets that Sentarou doesn't know. The lie that a target object was always needed was made to make the Union members believe they have a defense against the dog, when in fact they never did. It also puts an artificial limit on Sentarou.