In the case of Japan they were usually purchased from the Japanese. At first the Portuguese mainly purchased Chinese slaves in Japan, but from the 1570s Japanese slaves were increasingly purchased. Japanese entered slavery for numerous reasons, but one of the primary reasons was poverty and refugee status following the constant conflicts in Japan in the period. Later demand for Japanese slaves grew this was related to profitability, but there was also a large market for young female slaves for the purposes of sex. After Hideyoshi banned the trade, it continued based on labour contracts.

In the 1590s the Jesuits took a stand against it leading to a short-lived Portuguese ban on the trade of Japanese slaves - however the complaints of traders to the Portuguese court led to a compromise - traders were no longer allowed to illegally (forcibly) take slaves, but were allowed to take those who sold themselves into or were sold to them. Such debate suggests that prior to Jesuit complaints the Portuguese traders had also forcibly taken Japanese trade, but I don’t know of any sources that record this other than anti-foreign propagandistic Japanese pieces.

Sources:

Nelson, Slavery in Medieval Japan

De Sousa, The Portuguese Slave Trade in Early Modern Japan

Morris, Christian–Muslim Relations in China and Japan in the Sixteenth and Early Seventeenth Centuries