Very doubtful. Few parts from one car manufacturer will fit a car from another rival manufacturer.
However a few measurements could tell for sure.
First, they would need to use the same amount of lug nuts.
Then measure the distance from the lug nut to the center of the rim. Measure the diameter of the lug nut holes. Measure the diameter if the wheel hub opening in the center of the rim. Finally you must also measure the offset of the rim. This is the depth of the rim measured from the wheel hub mating surface to the inner tire mating side of the rim. If the rim is not deep enough it could hit against the brake caliper.
If all of the measurements match your current Toyota rim you can use the Mazda rim.
The link below may be helpful on how to correctly make these measurements.
www.rsracing.com