If a Chinese-American teenager was shot without cause by police, do you suppose that Asian-Americans would be out in the streets protesting, with some rioting and looting? Of course not, because Asian-Americans, at least in the last 60 years or so, don't have personal experiences with police.
That's not the most prominent reason why there is far less likelihood of rioting and looting among Asian-Americans.
There's a considerable difference in propensity toward violence between a subsection of the African-American community compared to the Asian-American community. For instance, I live in Indiana. Indianapolis annualy holds a Black Expo weekend. It's supposed to be a fun family gathering for a predominantly African-American crowd, but that event is annually marred by violence from young African-American males looking to create trouble (
link). It's these pockets of havoc bent young African-American men, not all African-Americans, who loot and riot during protests. Comparable pockets of young Asian-American men looking to create havoc are far more rare. This dynamic has little to do with personal experience with police.
You suggest that most African-Americans have had negative experiences with the police, and that may be true. If negative personal experiences with the police was the primary reason for looting and rioting, though, then wouldn't more African-Americans be rioting and looting?