When you put water on plate and heat, the heat is transferred to water and temperature of water is increased. Gradually water reaches 100oC, then further heat is absorbed as latent heat and phase change occur (become water vapour). Until total water is evaporated, paper plate is unable to catch water.
After water is evaporated, further heat is absorbed in order to reach ignition temperature of paper. As soon as paper plate reaches it ignition temperature, it catches fire.