Mixing two metals raises the liquid's entropy, lowering its free energy — so the melt stays stable to lower temperatures than either pure metal. For lead and tin the melting point bottoms out at the eutectic: 61.9% tin, 183 °C, below either pure metal.
At that single point one liquid freezes into two solids at one fixed temperature — the invariant reaction, degrees of freedom F = 0. It is the alloy world's version of a pure substance's sharp melting point.
Off the eutectic, cooling first grows primary (proeutectic) crystals — α on the lead-rich side, β on the tin-rich side — while the leftover liquid drifts toward the eutectic composition. When it reaches 183 °C that liquid freezes all at once into fine lamellar α + β that fills the gaps.
The lever rule reads the amounts straight off the tie line: above 183 °C the arms give liquid and primary solid; below 183 °C they give total α and total β. That's the whole diagram in one gesture.
Something in the simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.