Why do radioactive decay starts after rock solidifies?

It doesn't start after the rock solidifies. Radioactive isotopes decay whether they are in molten magma, solid rock, outer space, etc.

You may be confused about how radiometric dating only gives us information about the time since a mineral solidified. It only gives information after that point because prior to solidification, the radioactive isotopes and the daughter isotopes can flow all over the place. In order for radiometric dating to work you must have a closed system, which for rocks is usually going to mean a solid rock that hasn't undergone alteration (some types of alteration aren't really melting the whole rock, but can allow isotopes to escape or be added).

Zordoz is correct despite the negative vote - radioactivity goes on all the time - some of the products are gaseous or otherwise can migrate when it is molten - once it solidifies, the breakdown products are trapped and the relative amounts of source and breakdown can be measured to determine age.

Radioisotopes decay continuously, however, it is only after the rock solidifies that the decay products are captured for measurement.

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Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). A decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide, transforms to an atom with a nucleus in a different state, or to a different nucleus containing different numbers of protons and neutrons.