From the Tokyo reporter article, the two arrested have not been granted refugee status, but are in the process of applying for it:
TOKYO (TR) – Tokyo Metropolitan Police have arrested two Turkish nationals currently applying for refugee status for allegedly raping a woman in Kita Ward, reports the Sankei Shimbun (Feb. 22).
The suspects arrived in Japan last year. They applied for refugee status in August and October, telling the Immigration Bureau of Japan that they did not want to return to Turkey due to “problems that exist between relatives.”
While their applications were being examined, the suspects received a visa status granting “special permission to stay in Japan.”
While Japan grants only a small number of people refugee status, there is a far larger number of people living in Japan applying for refugee status. From Foreigners abuse refugee application process to continue working in Japan, written in October 2014:
Foreign interns and students are falsely applying for refugee status because they can work while a decision is being made on their applications, a process that could take several years.
Under the change in the law made four years ago, applicants with an approved visa can start working six months after filing for refugee status.
Some who have applied in recent years do not face persecution if they return to their home country, but filed because the drawn-out process means they can work those years in Japan for higher wages than what interns and students are paid.
According to ministry officials, in 2013, 544 Nepalese applied for refugee status, the second largest number behind Turkish applicants, who totaled 658.
From a more recent article: Subaru’s secret: Marginalized foreign workers power a Japanese export boom (July 28, 2015)
A key source of gray-market labor for Subaru’s suppliers is asylum seekers. In Japan, these people fall broadly into two categories: The bigger group of asylum seekers is made up of those who are allowed to work and have permits that need to be renewed every six months. A smaller group is made up of asylum seekers who are on “provisional release” from immigration detention and are working without permits. Under government immigration rules, these people are allowed to stay in the country while their asylum applications are reviewed. But they are not allowed to work.
Asked how people on provisional release were supposed to survive if they were barred from working, Hidetoshi Ogawa, a senior official at the Ministry of Foreign Affairs, said they should rely on support from their relatives, friends and local charities. He said provisional release was a humanitarian measure to avoid long-term detention, “but in truth, these people should leave the country.”
On a related note, this answer to a related question mentions that Japan has approximately 100,000 Muslims, of whom 10,000 are citizens.