The transfer of power and the tearing apart of the nation do not happen right away. Instead, this change is delayed until the next generation. The actual removal of the kingdom takes place specifically from the hands of Solomon's son [מלבי״ם].
However, the royal rule is not taken away in its entirety. The portion that is removed and handed over to Jeroboam represents the vast majority and the core of the nation, consisting of ten tribes [ביאור שטיינזלץ].