Correct. I've driven WagonR MT a million times and like it a lot for its transmission.
CVT has a delay with the rubber-band effect & it's a bit vocal as well & if you push it hard enough 'now & then' or drive it in other than 'D' mode - be mentally ready to visit workshops on regular basis.
Passo & all other JDM cars have CVT transmission. Yaris's no different. So, behavior will be same.
In AT, there's a serious lack of control. You can not drive it moderately fast. Either you can drive it slow or fast & then you need to fiddle around with the accelerator paddle to control gears. If you don't do it, it's either becomes very slow (in higher gear) or becomes too noisy (in lower gear).
Try maintaining 3.5K RPM in any AT car and you'll see what I mean & I'm telling this from 3 years of experience driving CVT.
Automatics (including CVT) tries to keep RPM in low rev-range, that introduces carbon problem. That is why, engines with CVT won't last long. It's true for PKDM engines. Read it more on this here.
But AT users, including myself, for the sake of convenience of AT transmissions are perfectly OK with this described behaviors as their main pain-point is rush-hour traffic & willing to pay higher for this convenience.
However, like I've said earlier, if you drive only within city limits where you don't need acceleration, breaking, etc., AT is pretty good. But as soon as you get outside of this particular scenario, you'll start to see these issues. But again, 90% people never go to hills, road trips, & their routine travel is so minimal that they like AT a lot.
Yaris MT can beat Yaris AT (both 1.3 & 1.5 AT) in acceleration, breaking & hypermiling so is the case with WagonR, Cultus, City, Corolla, Vitz, Ciaz, etc.
I remember a time, last year, when I couldn't compete with a friend when going uphill to Monal. I was on Altis 1.6 2017 AT and he was on GLi 2012 MT & we both were driving a bit faster.
That's my personal experience.