I take "AA heavy" with a heavy grain of salt. Relatively speaking, perhaps there will be a few more AA's than usual for Universal standards, but again I think an amount similar to POTC is a huge stretch. Every time a new Universal attraction is in the works, people oversell how many they will have. I've been around long enough to remember when Gringotts was supposed to have an impressive Voldemort AA according to some sources. Kong's AA's were also oversold during development. It also depends on your definition of "AA". People often mistakenly call mostly static figures AA's.
Unless this is old information, the Monsters ride is supposed to use the Kuka Arm ride system seen in Forbidden Journey. So presumably a fast paced ride with a lot of motion to the vehicles. Unless they change things up with that ride system for the Monsters variant, it's not a system that sounds like it would be likely to be mixed with a significant AA population. Forbidden Journey has a lot of physical sets, but there's not a whole lot of motion to those sets. Mostly just that one simplistic dragon figure and the Dementors (which don't really have motion of their own, but rely on the Kuka arms they're attached to along with fans blowing their cloaks to simulate motion). And i'd be hard pressed to call those "animatronics" since they have fewer axes of motion than some of the figures in classic Fantasyland dark rides.
The Ministry dark ride I think was described as similar to Tower of Terror where it can stop at different floors and even exit the vertical shaft to travel horizontally. Much like the elevator used in the Potter films. Again though, i'm hesitant to assume it will have a lot of AA's. It sounds like something they'd do with some physical setpieces but using projected characters. Kind of like the Gringotts preshow with Bill Weasley.
We already know what to expect from the Nintendo stuff. Mario Kart is physical sets with AR projections of the characters. Yoshi uses a handful of simple figures that don't qualify as AA's. The DK coaster blueprints have been leaked many times now and there's not going to be enough space for significant amounts of AA's (probably just one or two around load/unload at most along with mostly video projection). Maybe the HTTYD show will have a few AA's though, there was an existing stage show that went on tour that used some impressive puppets/AA's.