Rigor mortis manifests in cats at the same rate that it occurs in all mammals - after a few hours. When this occurs, muscles progressively stiffen until the body becomes stiff as a board. This state persists for 12-20 hours before the body becomes flaccid again and also begins to decay.
The cause of rigor mortis relates to energy supply in muscles. Muscles actually use energy to relax, which they do by breaking associations between the actin and myosin filaments that make up muscle. When an animal first dies, muscles are biochemically still metabolically active and so they have a ready supply of energy and can break any links between actin and myosin.
But, as time passes and cells run out of energy, this can no longer be done and the muscles "lock up". This is rigor. After another 10-15 hours has passed in this state, however, the cells and the contractile proteins begin to break down, which causes the return to a flaccid state.
In the question above the cat apparently jumped into the air several times despite the fact that it was dead. The most likely explanation is spontaneous muscle activation initiated by waves of nerve discharges in the brain and spinal cord which can be triggered by physical trauma or as a consequence of oxygen deficit.