The cafe owner told Associated Press that the suspected militant had been logged on to the internet for about five minutes when officers stormed in. Police said the suspect fired one shot from a revolver before he was killed.
In the second operation, police said they had shot dead two suspected members of the same group and arrested two more.
Anti-terror police chief Tito Karnavian told media the dead man from the first raid was a "big name".
A police spokesman, Edward Aritonang, later told the BBC it was not clear if the man was Dulmatin and that further tests were taking place.
He said: "We believe that the man... supplied weapons and funding to the Aceh militant group."
Indonesia's Metro TV station showed footage of what it said was the dead man.
Dulmatin has been one of the most-wanted Indonesian militant figures. The US has offered a $10m reward for information leading to his death or arrest.
He is believed to have set off one of the two bombs in Bali on 12 October 2002. A total of 202 people died in the attacks, many of them foreign tourists.
Officials have yet to confirm if the first man killed was Dulmatin
Dulmatin had been thought to be hiding in the Philippines.
Security ministry anti-terrorism chief Ansyaad Mbai told Agence France-Presse: "If it's true that it's him, we will be very grateful that the most-wanted terrorist has been killed. It will be a big relief to us."
DNA tests might be needed to confirm whether Dulmatin was the man killed.
Such tests were needed to prove beyond doubt that Noordin Mohamed Top, at the time Indonesia's most-wanted Islamist militant, had been killed in September 2009.
Police thought they had killed him in a previous raid only for forensic tests to prove them wrong.
Dulmatin was also rumoured to have been killed previously - tests were carried out on a body found in the southern Philippines in 2008, but it was confirmed to not be his.
The latest raids come less than two weeks before the visit to Indonesia of US President Barack Obama.
Police check the scene of the second raid, where two people died
Indonesia has made significant inroads in recent years into dismantling the leadership of Jemaah Islamiah.
The police have also been recently engaged in an operation targeting Aceh militants.
A total of 14 people have been charged with plotting to launch terrorist attacks.
Those charged are believed by officials to be members of a previously unknown terror group.
But seizures in raids included DVDs on the Bali bombings.
Police have been investigating possible links between the militants and Jemaah Islamiyah, which was blamed by the authorities for the Bali attacks.
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