When and went why did Asian Americans go from "yellow peril" to "model minority" in the minds of white Americans?

This is actually a more fragmented shift than the question presupposes. There wasn't a point where you could say they all fit in either of these two categories according to most Americans. In other words, there's a slight problem with the premise.

In the late 1800s after the Opium Wars and the lead-up to the Chinese Exculsion Acts, the Yellow Peril was in full swing, exemplified in things like Sax Rohmer's writings and the sort of rhetoric that was developing against Chinese on the West Coast. This was coming right after the quickly-modified 1868 Burlingame Treaty which had, albeit briefly, encouraged Chinese immigration to the US, and things like the Boxer Indemnity funds which also resulted in Chinese students coming to the US. However, as mentioned it was quickly reversed, in part, as the Angell Treaty signed in 1880, which we can say is the formal start of anti-Chinese legislation on a national level.

But this did not generally apply to Japanese. At the same time that Chinese were being marginalised with attitudes toward them becoming negative, Japan was still fetishised in a popular light, and just after the turn of the century it wouldn't have been at all uncommon for the average white American of means to engage in things like sushi parties. The Page Act (1875) did include Japanese by name, but this was more intended (as written) to prevent unwilling migration, and at any rate the number of Japanese migrating at the time was nearly infinitesimal. The Page Act was fairly limited in scope, and it would be a mistake to take it as the most indicative thing reflecting how white America felt toward the relevant cultures at the time.

I digress. While the situation for Japanese wasn't the same everywhere, most notably in Hawai'i where there was a stronger resistance in the late 19th century, it wasn't really until well after the Chinese Exclusion Acts were at their height that the tables turned on Japanese immigrants, having been somewhere between tolerated and accepted up until then. It wasn't really until the Immigration Act of 1924 that Japanese were explicitly banned, though due to economic competition there was plenty of hostility growing in the two decades before then. While in the end they ended up caught up in the Yellow Peril, they really were separate from the whole thing for the first good many decades.

So that's one end, the Yellow Peril end, of the spectrum you've proposed.

For the other end we can look at the 1980s and 1990s where Chinese immigrants, now quite well established, were seen in terms of the "model minority", but again this did not apply to all East Asians. Koreans and Vietnamese still had significant difficulties, though where they fell on the scale fluctuated with time and place. During the LA riots, Koreans were very much not seen as the "model minority". (edit: I need to clarify that this wasn't a causal relationship so much as, during that time, views on Koreans were mixed among the average white American. That the riots happened and brought people's attention to them is coincident, but not necessarily a determiner of negative attitudes. It's in part because they were seen as heroically defending shops, as one commenter brought up, their image fluctuated into the positive.) Likewise Vietnamese immigrants/refugees in the 1980s and 90s were accused of all the same claims that they were unassimilable with America's culture that the Chinese had faced a century before. Regardless, at this time, Vietnamese immigrants included into the category of "model minority" for most white Americans, where Korean Americans fells in that scale was also not clear, and still when the riots were happening, Vietnamese immigrants who had little or nothing to do with the LA Korean communities were also targeted.

The divisions between East Asian groups, as viewed by White America, were always more salient in the public eye than their shared Asian-ness. You can see this most strikingly comparing characters of Chinese (and Japanese) near the beginning of the 20th century with the sorts of WWII-era illustrations, for example "How to tell a Chinese from a Jap" where now the Chinese are described as more "normal" in comparison.

Attitudes toward different East Asian groups have been constantly shifting for as long as there have been Asians in North America, and chances are that will continue to happen.

It's late so I've not included a lot of specific details and listed references here but if you want to know more about any of the above points, please let me know and I'll be happy to fill in more detail as requested. It might take a couple days though because I'll be travelling internationally and I'm pretty sure my planes won't have wifi.

Sources:

Korean Americans in the 1990s:

Elaine Kim's Home is Where the Han Is: A Korean-American Perspective on the Los Angeles Upheavals, as mentioned by /u/The_Alaskan, is a great place to start for those interested in that period.
Abelmann & Lie (1995) Blue Dreams: Korean Americans and the Los Angeles Riots — same period

Vietnamese refugees and immigrants

Barkan, Elliott R, (2012) Immigrants in American History:Arrival, Adaptation, and Integration — (among other groups)
Schulzinger, Robert D (2006) A Time for Peace: The Legacy of the Vietnam War

Chinese Exclusion Period:

Gyory, Andrew (1998) Closing the Gate: Race, Politics, and the Chinese Exclusion Act
Lee, Erika (2003) At America's Gates: The Exclusion Era, 1882-1943
Mar, Lisa Rose (2010) Brokering Belonging Chinese in Canada’s Exclusion Era, 1885–1945. Oxford University Press.

Japanese Americans: (mostly Hawai'i but also addresses mainland issues)

Okihiro, Gary Y (1991) Cane Fires: The Anti-Japanese Movement in Hawaii, 1865-1945
Odo, Franklin (2004) No sword to bury: Japanese Americans in Hawai'i during World War II

Related Reddit comments (further reading) – I've written a dozen or so answers about topics related to Asian immigration to the Americas. The following are the one I dug up which may be most relevant, to which I would have ended up saying similar things in this comment, but it's probably better to just link in the interest of parsimony.

Anti-Japanese sentiment as related to the period of fetishisation (actually about the history of sushi in America but touches on these issues)
What was the impact of the Great Depression on Asian Americans?
On the United States' Chinese Exclusion Act and related anti-Chinese immigration policies
Were Vietnamese refugees subject to racial violence in the United States?

A note regarding sourcing answers on AskHistorians: (speaking as a mod)

^(Speaking as a mod for a second: Sources are not a requirement at /r/AskHistorians for top-level comments, unless they are requested. I only just now saw that two people have reported this comment for lacking sources, but no one had actually asked for a source, so none were included. I did say, just one paragraph above this, that I would happily provide sources / more info. I didn't actually see the comment reports until just now, because – again since sources aren't required – other moderators approved the comment thus marking those reports as "read", so to speak.)

^(However since I've now seen the reports, I'll take that as a request and have provided some above. For future reference, if you see a comment that you'd like sourced but isn't sourced, don't report it because the commenter never sees that. Instead, leave a reply asking for sources. )