i know the problem. basically it's nothing to do with the CVT and there are a few problems that might have the same symptoms. i will list down most common ones first:

1. sparkplugs: Honda City 1.5 CVT uses iridium plugs. According to honda the plugs have lifespan of 100,000km but have known to be faulty even at 60k if you constantly rev over 5k RPM. mine died at 70,000km because i'm a vtec person.
symptoms: doesn't cause that much vibration but you will notice the RPM will dip suddenly causing the car to jerk at times when idling and also when slow accelleration. many have feared that their CVT have problems but this is not the case. just change the plugs. not any plugs because you have to use the same factory NGK iridium plugs. Damage: RM200+/set
Solution: replace

2. intake are control valve (IACV): most common issue associated with RPM drop when stopping, also when your aircon compressor kicks in. This version of honda city do not use an electronic sensor, the IACV is more of an actuator that controls the air flow to maintain stable idling. It controls air when you press on the brakes, turn your steering wheel, aircon kicks in, putting in D, etc. pretty much everything. this module rarely spoils but it can get dirty causing unstable idling when you do one of the above. if left unchecked, it can also lead to flywheel problem which is your next problem.
symptoms: RPM drops rapidly when you brake, compressor kicks in, turn your wheel, put on D.
Solution: just need to clean it but that's the tricky part. the IACV is screwed onto the throttle body with 4 security torx screws and no workshop have the key to open it. Honda CC will not bother to clean it for you and most probably ask you to change the entire throttle body. After some pain aching time, i got my friend to buy the security torx screw set for his workshop and i fixed the problem there.

3. flywheel: the CVT version uses a flywheel that sort of looks like a clutch, torque converter combo. There are 4 springs on this thing that can get loose over time. if this happens, it will increase the vibration and cause some crackling sound then the RPM drops too low.
Symptoms: most noticable when you put on reverse. RPM drops and engine seem to vibrate uncontrollably. you will hear the some crackling sound (that's actually the sound of your flywheel) just before your gear frees itself automatically and the RPM kicks back up by your ECU. This feature is meant to protect your engine and transmission but can get annoying at times.
Solution: change flywheel set for RM1400 at any Honda CC.
Honda City CVT issues: earlier models had issue with CVT but is only associated with aeroplane noises when idling and cruising. This problem was fixed and no longer present itself after the 2005 model. i believe they made the steel belt bigger and stronger. Many are also caused by workshops unfamiliar with CVT and used ATF when they should have used CVTF. Just make sure you service and replace the CVTF every 18,000km and you are safe. My Honda City Vtec 2007 model is already nearing 300,000km mileage and the CVT still works perfectly.