Basically, here is what happened:
[Polish refugees] discovered that two Dutch colonial islands, Curacao and Dutch Guiana, (now known as Suriname) situated in the Caribbean, did not require formal entrance visas. Furthermore, the honorary Dutch consul, Jan Zwartendijk, told them he had gotten permission to stamp their passports with entrance permits.Sugihara's role was that he issued thousands and thousands of transit visas, ignoring his annual quotas (which he was often filling daily). Through his efforts, against the orders of his superiors, many of these Jews were able to escape.
There remained one major obstacle. To get to these islands, the refugees needed to pass through the Soviet Union. The Soviet consul, who was sympathetic to the plight of the refugees, agreed to let them pass on one condition: In addition to the Dutch entrance permit, they would also have to obtain a transit visa from the Japanese, as they would have to pass through Japan on their way to the Dutch islands.
There's even a database where you can search for survivors.