Mini-spit AC unit consuming electric power when off
Your old system did draw current but your measurement equipment was probably not sensitive enough to measure it. If there is a remote to control and activate the system it has to have some power to do this.
Your new system being an inverter based system is also always drawing power the control buss is usually powered up to maintain the charge on the capacitors if it is powered down it will take an average of 30 seconds up to 3 minutes to deplete this charge and to wake the system up takes longer than when in standby and is harder on the electronics.
Where your new system will out preform a single speed system is it can maintain the coolant/ heating levels without starting and stopping all the time but running at a slower rate using less energy overall.
So yes your inverter based system is probably drawing 270ma but this is how that technology works just the elimination of a few hard startups a day will more than compensate for the small draw when not in use.
And your equipment was not sensitive enough to measure the 15-20 ma of Curren draw in your old system if the remote can turn it on there is current being consumed.