At the climax of the meeting between Joseph and his brothers, the dams of restraint finally break. The deep, private emotion that Joseph had bottled up for so long is no longer confined to a single room. Instead, it overflows, echoing outward until it reaches the highest levels of the Egyptian government. Letting go of all control, Joseph releases his feelings completely [רש ר הירש]. Unlike earlier moments when he had to leave the room to weep in secret, he now cries loudly right in front of his brothers [ביאור שטיינזלץ].
Normally, the sound of crying does not travel far. However, Joseph made a great effort to raise his voice to speak, and his tears burst forth, amplifying the volume [אלשיך]. He revealed his identity to them from within a fierce emotional storm [העמק דבר]. This loud, unrestrained weeping also served as a clear proof of his sincerity to his brothers, as such intense emotional turmoil is nearly impossible to fake [רש ר הירש]. On a deeper, hidden level, the specific nature of his weeping serves as a hint to the future, final redemption of the people of Israel, which the prophets foretold will also be accompanied by tears [שפתי כהן].
Although Joseph had ordered all the attendants to leave the room before revealing himself, the Egyptians had only stepped just outside the door. Standing so close, they were the first to hear his loud cries [רד״ק, רשב״ם, רלב״ג, ביאור שטיינזלץ]. From there, the news quickly rolled forward. The rumor that Joseph was weeping, and eventually the news that he had found his family, spread rapidly from person to person until it reached the household of Pharaoh [רד״ק, רלב״ג, העמק דבר, אוהב גר].
The primary approach among commentators is that the household of Pharaoh does not refer to the physical palace building itself. Rather, much like the terms House of Israel or House of Jacob, it refers to the people of Pharaoh's court, his servants, and his family [רש״י, מזרחי, ריב״א, גור אריה, ביאור יש״ר]. The very fact that the entire royal court took such a deep interest in Joseph's private emotional storm, even before they knew the exact reason for his tears, stands as a powerful testament to his high rank and the immense respect he commanded throughout Egypt [רש ר הירש].