No, the tsunami was not caused by the idol which was thrown into sea in the 12th century. The butterfly effect here means everything is connected. That incident is not the cause of the tsunami. But the incident of throwing the idol has connection with the Tsunami occurring in 2004.
Butterfly effect is defined as:
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
Explaining what is Butterfly effect in the movie is lengthy. For that we should know entire movie plot along with characters. Writing that here would make answer too much lengthy. But here's the Butterfly effect briefly.
The movie starts with Tsunami relief programmes and Bio-scientist Govindarajan Ramaswamy speaking about butterfly effect and chaos effect. To explain what happened, he goes to 12th century and the history of the Perumal idol placed on dais. He explains the history of what happened in the past.
Kamal Haasan played 10 different roles in the movie. Every character is not related in any way. But due to course of events, each character affects the events and different characters meet some or the other way.
In his journey to save the vial from terrorist groups, Dr.Govind meets different people who are unrelated but their small actions knowingly or unknowingly drive the plot and lead to the day Tsunami occured.
Surprisingly, some parts of the movie and the end of the movie also relate something to 12th century. It's shown that Tsunami has occurred to save people and decreased the affect of the vial by great margin. It also shown that God had helped different characters in different ways which took place in the course of Tsunami.
The Govindarajaswamy idol is submerged into the sea in 12th century. The processional deity (utsavar which is referred to as Perumal) plays a major role in the film and shown in the beginning of the film on the dais.
Govind's colleague Suresh's wife Yukha Narahazi is killed by Fletcher. Her death is avenged by her brother Shinghen Narahazi. He comes to India to kill Fletcher. But Fletcher kills himself by swallowing the vial. After the relief, he leaves a necklace as a remembrance of his sister.
The Muslim family and people gets saved from the Tsunami when they take shelter in the mosque.
Avatar Singh, the pop singer gets cured of his throat cancer by a bullet fire by Fletcher.
Vincent Poovaragan, social activist works for the eradication of sand mafia at a place where final rites of Rangarajan Nambi from twelfth century were done before throwing into the sea. Nambi's wife is dead there and her sacred thread is also shown. After the Tsunami, Krishnaveni Patti thinks Vincent is her dead son and lament for him. In this way, the deep sorrow for her son accumulated in her heart is removed.
George W. Bush: The 43rd U. S. President is also a character in this film because the initiative was taken by the U.S government to create a weapon without knowing its potential. Later he visits India and congratulates Dr.Govind for stopping the mass destruction.
After relief, Andal argues that god had sent forth the tsunami to get rid of the weapon. Govind responds by asking if god would destroy hundreds of lives to save millions. Then, they are later revealed to have been talking in front of the idol submerged in the 12th century. So, it came to the place where all it has started. Hence we are shown that everything is related - which is the concept of Butterfly effect.
To symbolize the butterfly effect, a butterfly flapping its wings and traveling from one place to others where characters are standing is shown in the end. But for better understanding of what is the butterfly effect and how the action of one character affects another (or mainly Dr.Govind because he is the protagonist), we have to watch the film.