CE-680 Captain reported encountering wake turbulence on descent into MIA in trail of an A319. Reporter expressed concern that MIA Controllers were not showing appropriate concern about wake encounters.

Narrative

We were on the VIICE2 arrival. We were 5 miles in trail of an A319 Airbus. Passing through about 7300 ft. we encountered wake turbulence. We were rolling left and we were full scale deflection right; the right seat pilot was flying and did a great job. We advised ATC and she cleared us to offset right we still encountered it; a little worse this time. [Then] she cleared us on a vector for a visual approach [and] we completely got out of the wake. [A few weeks later] we departed out of Miami [and] the Tower gave us immediate right turn approximately 3 miles in trail of an A321. We did not have any wake turbulence; but the Departure Controller immediately vectored us off; she knew we were way too close to him. The passenger commented on this; and told us 'good job'. One wake turbulence event; and one way [too] close on separation in Miami airport; in my mind [this] is very dangerous. There's a lot of big airplanes at this airport and it seems like more and more we have to rely upon ourselves to stay away from these airplanes and not get flipped upside down. Controllers and pilots need to be more aware of wake turbulence. I don't think wake turbulence is talked about enough; I think it should be taken more seriously by all involved.