(Note: I don't have a graduate degree in history, but I focused on constitutional law and history in law school.)

This is a great question, but in many ways it is unknowable. "[T]urn from" suggests a fundamental transformation, but this might not be the case. Japanese internment isn't a discarded relic of constitutional jurisprudence. Korematsu, the case affirming internment, remains good law. It's precedent, and unless it is overturned or distinguished, a national emergency (at least as perceived by military commanders) is a sufficient basis for making otherwise impermissible racial classifications. That is to say, Japanese internment isn't a blight in modern civil rights law, it's a permissible exception.

If Warren transformed, it may have been due to (1) electoral politics, (2) court membership, and (3) his conscience. The last first, since its evidence is thinnest. In his memoirs, Warren regretted his implementation of the internment order. He stated that "[i]t was wrong to react so impulsively, without positive evidence of disloyalty," and he was wrong to do so. When pushing for a unanimous ruling for Brown v. Board, he invoked that moment as a mistake in order to ask fence-sitting judges to side with history. His back-and-forth drafts with skeptical judges indicate that he's worried about any precedent that's not crystal-clear, and he is concerned with how minor differences between a majority and dissent (or even concurrence) could be used to erode rights.

But (1) electoral politics might be a better explanation. Warren holds a nearly-unparalleled position in California's history. California's constitution now bars governors from serving more than two terms. Warren, along with current Governor Jerry Brown (grandfathered in by the constitutional change) was elected to a third term. Unlike Brown, he was an overwhelming favorite. Due to party fusion being allowed at the time, Warren was nominated by the Republicans, the Democrats, and another party. He carried over 90% of the vote. This is unthinkable to modern elections. His first gubernatorial election wasn't such a landslide, but he beat the incumbent governor by 16 points (57-41). The incumbent governor, an avowed liberal atheist, was the rare opponent of internment but he later relented and supported the move. It's possible that Warren, as AG, was looking for a break with the current governor on a "hot" issue that moved voters. It's also possible that he was caught up in the issue himself, as a coastal resident during wartime.

As governor, Warren didn't fight civil rights. When California's marriage laws became the first in the nation struck down on anti-discrimination grounds, Warren didn't protest. (Interesting note here: the case involved a Hispanic woman and a black man, and was barred under the contemporary understanding that Hispanic residents were "white.") Courts invalidated racial discrimination in California schools (CA didn't actually have a statewide system of Hispanic-Caucasian school segregation because they were considered the same race, but counties in the south had an informal implementation of this practice) and the CA legislature repealed the existing school segregation laws; Warren had a signing ceremony to showcase his support of this repeal.

As for (2), it's important to note what the Supreme Court looked like at this time. When Truman left office, every justice was appointed by FDR & Truman. The New Deal coalition ran the Court. Fault lines ran across economic issues more frequently than social issues, and social issues were often divided along lines that are unfamiliar to us today. (Notably, "structural" constitutional structure was often considered. If laws altered the formal balance of power in the Constitution without tampering with the relative power of branches, the laws were typically allowed. Legislative vetoes and delegation fell in this area, but so did more typical social issues. Plus the liberal use of social science data meant that originalism, as we know it today, didn't factor in.) It was easier for Warren to gain consensus because he wasn't at the court's left-most margin. Douglas was much more liberal than Warren, as was Marshall later on. While Warren commanded opinions for Brown v. Board and Loving v. Virginia (and an impressive majority-concurrence-concurrence-concurrence for Gideon), Warren didn't always have that backing.

Warren's approach on crime issues was often more nuanced, and more reflective of his time as AG, than his other cases. While he championed the right to an attorney in Gideon and Miranda rights, he wasn't as sympathetic to rights for suspected criminals that didn't necessarily touch on poverty, education, or race. Most notably, he sided with stop-and-frisk policies in Terry v. Ohio, which have achieved notoriety in recent years. Warren also joined an opinion about 4th Amendment rights that has been increasingly difficult to apply as technology changes (basically, as your personal expectation of privacy decreases, so do your rights to private communications).

So how did Warren turn from internment implement-or to civil rights stalwart? Maybe he was worried about voters while seeking higher office, and he turned after his election. Maybe his conscience actually got to him, and that's why he changed after being elected governor. Maybe he didn't change at all; internment was followed by his law-and-order emphasis in later cases, and internment precedent remains good law.