There is a strong likelihood that the ANZ could tweak rates up or down 5 or 10 basis points each month regardless of what the RBA does, but rather according to trends in funding costs and demand for credit. And this is entirely reasonable. Financial markets ructions and the broader funding sources for banks means that the cash rate - for now at least - is less relevant to the interest rates you and I pay on our loans or receive for our deposits. Right now, you can get 6.0% of a 6 month term deposit - a whopping 175 basis points above the cash rate. Great stuff for savers and perhaps more importantly a sign of just how tough or rather how expensive alternative sources of funding are for the banks.
I am pretty sure the banks wouldn't be paying those sorts of interest rates on deposits if other funding sources were either cheaper or available at the official cash rate. To highlight this shift of focus, one only has to look back at term deposit rates versus the cash rate prior to the GFC (when money was freely lent to any Tom, Dick or Harry - few or no questions asked). Back then, there were almost no examples of banks offering terms deposits above the cash rate and in fact the margin below cash was often triple digit basis points.
The end point of this is that the game is changing. It's too early to be sure how it will evolve - but the increasing focus of the RBA when it sets the cash rate will be where retail lending rates are. If funding pressures force lending rates up and the RBA sees this as unwelcome with reference to its inflation target, it will cut the official rate more than otherwise to try to bring retail rates lower - and vice versa. It will be fascinating to see how the new order pans out.