These transmissions don't have gears as they're CVTs (continuously variable transmission). It's a steel belt which provides the transfer of power between the output/crank shaft and the final drive. The output shaft and final drive are variable pulleys. These pulleys are made up of two pieces which form a V shaped channel. The pieces slide in and out to adjust the width of the V. The steel belt sits inside of this V. As the width of the V adjusts the belt moves up or down in this channel. This action simulates different gear ratios. The movement of the halves of the pulley are controlled by hydraulic pressure. So the "shifting" you're feeling seeing is all simulated. This was done because people didn't bother to understand how CVTs operated and why they're different than a geared automatic transmission. People kept complaining to their dealerships about what they thought was the trans being stuck in gear. A CVT without the simulated gear shifts would just keep the engine RPMs at the optimal part of the power band constantly. So from a dead stop, the engine RPMs will just rise and hold at a certain point while your speed keeps picking up.
What I've described above is how all CVTs operate no matter which manufacturer. The new Corollas have a hybrid transmission where they have a physical first gear. Our transmissions are made by a Toyota subsidiary called Aisin. While this reported failure is a bit disconcerting, it's by no means the same concern I would have if our trans were made by Jatco. Jatco is Nissan's transmission subsidiary. It's well known Jatco CVTs are ticking time bombs and have been for years.
About 6 months ago, I noticed my trans was "shifting" a little rough. But it was brief and hasn't done so since. These transmissions are "sealed" units which are supposed to have "lifetime" trans fluid. So no maintenance intervals. But I plan on having the fluid changed in my trans around 30k miles. I normally would do this service myself but the procedure to do the trans fluid is quite involved. The fluid refill requires the trans oil to be at a certain temperature. So the car has to be level and running while you're filling the trans. At the rate I'm going, it'll be some time this year I'll need to have the service done. I'm at a bit over 21k miles now and I've owned my car for just over a year. We'll have to see how things go with the reliability of these trans. Fortunately, we do have a 5 year 60k mile drivetrain warranty.