The US didn't intervene because Japan was perfectly able to intercept the missiles and chose to not do it.
Japan’s J-Alert warning system advised people across a large area of northern Japan to seek shelter. Japan’s self-defence forces did not attempt to shoot down the missile and there were no reports of damage from falling debris.
The reason why Japan didn't intercept the missile was that they quickly measured its trajectory and concluded that it wouldn't hit them. I believe they preferred the missile to fall into the Pacific instead of having pieces of it raining on their cities.
EDIT: In response to a comment below doubting Japan's ability to intercept missiles, here is information about missile interception country by country, emphasis on the relevant part :
In 2016, the Japan Air Self Defense Force (JASDF), and also the Japan Ground Self Defense Force (JGSDF), initiated their 52nd year of annual live-fire missile launches at McGregor Range, New Mexico in Fort Bliss. The 2014 annual service practice of the PAC-3 Patriot missile demonstrated a 100 percent kill rate before a group which included the commanding generals of White Sands Missile Range (WSMR), and of the 32nd Army Air & Missile Defense Command (AAMDC). Every JASDF Patriot team participated in the annual exercise, which takes several months.
Since 1998, when North Korea launched a Taepodong-1 missile over northern Japan, the Japanese have been jointly developing a new surface-to-air interceptor known as the Patriot Advanced Capability 3 (PAC-3) with the US. So far tests have been successful, and there are planned 11 locations that the PAC-3 will be installed. A military spokesman said that tests had been done on two sites, one of them a business park in central Tokyo, and Ichigaya – a site not far from the Imperial Palace. Along with the PAC-3, Japan has installed the US-developed Aegis ship-based anti-ballistic missile system, which was tested successfully on 18 December 2007. The missile was launched from a Japanese warship, in partnership with the US Missile Defense Agency and destroyed a mock target launched from the coast