iDSI is the engine technology not transmission type,
City 2005-2006 came in 3 variants,
1.3 manual (which is called iDSI in our market)
1.3 cvt (called Vario in our market)
and 1.5 i-VTEC(non-iDSI) cvt (called steermatic)
It was very difficult for our mechanics to sync the load(calculated by amount of throttle and the output achieved) parameter between cng kit, ecu and tcu in cvt cars by our mechanics because cng changes the response of the engine and numbs the ecu from some sensors when driving on cng which in turn can't operate transmission properly so it results in early failure of transmission.
In short, if buying 2005-2006 city, you are better off going for a manual one, a cvt on cng would eventually fail in the hands of our mechanics whether immediately or if it was managed to run right already, it'll start problems after a "tune up".