A bank will similarly price its deposit rates based on the cash rate for an at call deposit, as they are alternative sources of overnight funding. For term deposits, again a bank will price them based on the expected future path of the cash rate.
The increase in these prices spills over to non-food and non-fuel (or the core) inflation through both higher input costs and higher inflation expectations getting reflected in wage revisions. In the presence of strong demand conditions, the spillover could be faster, to cause a generalised inflationary process.