The main reason that eating salty foods makes a person thirsty is that additional fluid is needed to

to dilute the salts and maintain the balance of water

Eating salty foods make our blood saltier and the fluid outside our body cells saltier, too. The thirst center gives a signal that the body needs additional fluid to dilute the salts and maintain the balance of water inside the body. It is during this time the person starts to feel thirsty.