I doubt that the UC improvements in USNWR ranking have much to do with being admitted to the AAU in 2019 since that is not a direct factor in USNWR ranking. In your comparing to 2020 list 3 of the UCs you had no change, 2 change by 1-2 spots, 2 changed by 3-4 spots, and 2 changed by larger amounts. I listed the 2 that changed by 5+ spots below.
Comparing to 2020
UCSC – Decreased from 84 to 97
UCM – Increased from 104 to 98
Comparing to before the AAU in 2019 shows UCM had huge improvement in rankings, and UCSC had a huge decline. Both UCM and UCSC continue their improvement/decline in 2019 and 2020. The change from 2020 to 2021 above is continuing a trend that began in earlier years. UCM improved 32 spots in 2020, then another 6 spots in 2021. UCSC declined by 14 spots in 2020, then another 13 spots in 2021. I am not familiar enough with the schools to guess at why the change in USNWR ranking is occurring at these 2 schools, but I doubt it has much to do with AAU admission.
The others 7 had relatively little change in both 2019 and 2020. Overall 6 had a decline in rankings since 2019, and 2 had an improvement. I don’t see much pattern. It’s certainly nothing suggestive of AAU admission improving ranking. It probably has more to do with the USNWR methodology changes in this period.
Comparing to 2019
UCM #136 to 97 (large improvement)
UCSC #70 to 97 (large decline)
UCSD #41 to 35 (small improvement)
UCSB #30 to 34 (small decline)
UCR #85 to 88 (small decline)
UCI #33 to 35 (small decline)
UCD #37 to 39 (small decline)
UCLA #19 to #20 (small decline)
UCB #22 (no change)