Shimazu Toyohisa was a historical samurai who died commanding the rearguard at Sekigahara for the Shimazu forces.

In the Sengoku a lot of daimyos passed law codes, at least some of which included laws prohibiting raping, looting, pillaging, and fighting. While I don't know if the Shimazu clan did, I wouldn't be surprised if they did. We know therefore that 1) it happened and 2) the daimyos know of the destruction and problems it would cause in the realm if these were not stopped.

However, as pointed out here, all bets are off if you're in someone else's realm.

Luis Frois said, when comparing Europe and Japan:

Our kings and captains provide soldiers with a salary; in Japan everyone must pay for his own food, drink, and clothing during the course of a war. Among us, one goes into battle to take places, cities, villages and riches; in Japan, the fighting is almost always to take wheat, rice and barley.

I am not (and I don't think anyone is) sold that Europeans armies did not pillage. But Japanese armies most definitely did.

The Shimazu clan was no different. In his History of Japan, Frois said (I'm translating from the Japanese translation of the Portuguese original):

In the previous year the villages and hamlets of Usuki [modern Usuki city, Ōita prefecture] was surrounded by the army of Satsuma [Shimazu clan] and burnt down, leaving only the castle.

Thomas Nelson, translating from the original Portuguese:

Some of the people seized in Bungo [Ōtomo clan] by Satsuma troops were taken to Higo [province] for sale. However, the people of Higo were suffering from terrible famine and travails at that time and could not even support themselves, still less the people they had purchased. Thus they [the captives from Bungo] were shipped off for sale in Takaku [Shimabara peninsula, modern Nagasaki prefecture] like sheep or cattle. In this way, they were sometimes sold off in lots of forty at Mie [in modern Shimabara city] and Shimabara. They were handing over women, little boys, and girls from Bungo for only two or three mon. The number of people sold was great indeed.

Fujiki Hisashi included in 雑兵たちの戦場 中世の傭兵と奴隷狩 (The Battlefield of Common Soldiers-Mercenaries and Slavers of the Middle Ages) many, many more mentions in primary Japanese sources of taking captives and selling them into slavery from clans across Japan, including the Shimazu.

There's no mention of rape. However I think since they were selling women into slavery (at bargain price) we should take it as it was so common to not worth mentioning.

I don't think it's possible to know what Toyohisa himself would have thought. However, there's no evidence that the Shimazu clan was any different and lots that they were every bit as brutal as all the other the clans in the Sengoku. Frois' passages from his History of Japan above was talking about the fighting between the Ōtomo and the Shimazu in the late 1570s till the late 1580s, the later stages of which Toyohisa (born 1570) took part. He certainly didn't do anything to stop the brutality. Not that he, as a young man who was just declared adult, could have.