Given the rule change, I suspect that the list won't change too much. It's too much legwork to see how private funding profiles have changed from 2018 to 2019 beyond the big money donations that make headlines. That said, looking at NIH funding for medical schools is pretty straightforward with the NIH Reporter system.
The 2019 rankings most likely used the funding data from FY 2017 as 2018 was barely getting started when the rankings came out in April. Here's the top handful of institutions by NIH funding for FY 2017.
JHU $651,844,903
UCSF $593,909,890
Michigan $521,788,658
Penn $493,869,965
Pitt $485,268,079
Stanford $465,856,075
UW-Seattle $443,367,966
Duke $440,306,575
WashU $435,637,200
Yale $425,247,606
UCSD $424,405,801
UNC-Chapel Hill $419,977,336
Columbia $402,667,654
UCLA $401,246,794
MGH (HMS) $394,465,880
BWH (HMS) $390,450,002
NYU is down at 33 with 233 million.
Here's the top 15 or so institutions by NIH funding for FY 2018
JHU $674,583,550
UCSF $647,880,065
Michigan $552,433,992
Pittsburgh $536,502,831
Penn $511,419,097
Stanford $505,474,358
WashU $486,295,442
Duke $475,338,515
MGH (HMS) $465,776,958
Columbia P&S $464,799,343
UCSD $459,093,333
UW-Seattle $455,841,035
Yale $454,012,666
UNC-Chapel Hill $446,660,231
UCLA $409,733,609
BWH (HMS) $388,928,321
NYU Medicine is down at 26 with 260 million in NIH grants. Here's that same list again for FY 2019. 2019 is in progress so these numbers are comparatively smaller.
Subtracting FY 2017 from FY 2018 to see changes in NIH funding, not exact but rounding by eye:
JHU +20 mill
UCSF +50 mill
Michigan +30 mill
Penn +20 mill
Pitt +50 mill
Stanford +40 mill
WashU +50 mill
Duke +35 mill
Columbia P&S +60 mill
UCSD +30 mill
UW-Seattle +10 mill
Yale +30 mill
UNC-Chapel Hill +30 mill
UCLA +8 mill
HMS has been excluded since in reality it's several institutions all smashed together and has far and away the most NIH funding of any institution (if MGH opened up it's own medical school and NIH $$ were the most important metric for the research ranking, they would instantly be a T10 school....and HMS would still be #1. Process that for a second).