Well I'm not any expert on Tin, but typically, when melted stuff is allowed to cool rapidly (or forced to), the resulting crystal structure, is likely to be affected, and that would also tend to alter transition Temperatures.
Ordinary "metallic" Tin, usually called beta-Tin, is a tetragonal crystal lattice, with just one atom per unit cell; two equal short axes, and one longer one. It follows C, Si, Ge, in the periodic table group 14. The other three, are cubic crystals that form in the diamond lattice, and are semiconductors. Tin also forms a cubic crystal in the diamond lattice, which is a face centered cube, which has four atoms in the unit cell. This form is called Alpha-Tin, and is the stable form at low Temperatures, and also is a semiconductor.
During Napoleon's ill-fated invasion of Russia, the Tin buttons on the French uniforms, morphed into Alpha-Tin, at the sub zero winter Temperatures, and turned into a grey powder. This left the French troops with their coats unable to be buttoned up, and many of them quickly froze to death as a result.
So it appears, that Tin has a mind of its own, and may not act as you expect, if you let it cool too quickly. In a past life, I was involved in the synthesis and crystallization of single crystal Gallium-Arsenide, using the horizontal Bridgeman gradient freeze method. We melted the components in an evacuated ampoule, and then linearly cooled it, with a lengthwise Temperature gradient, so that crystallization started at one end, which was seeded, and slowly progressed to the other end, taking about three days in the process. This formed single crystals in the Zinc-blende lattice (similar to diamond), and in the process, any impurities in the ingredients, were swept along the melt, by the partition coefficient, which preferred to keep the impurities in the liquid phase, yielding a crystal, with high purity except at the butt end, where the impurities were frozen out.
This is a case, where the very slow controlled Temperature linear cooling, is actually doing something useful, that simply takes time to happen.
So I wouldn't pooh-pooh the experiment instructions, in the case of your Tin melt, or you might get a surprise result.