If you were applying for a highly skilled job requiring complicated previous knowledge (e.g. captaining a ship, carrying out brain surgery), I'm sure INZ would check every detail of what you said you had done before. However, your responsibilities in the kitchen, as listed on the ANZSCO link above, are very ordinary things that any adult can be expected to have learnt at home and in the course of their general school education, so I doubt they would follow up more than your past month with your present boss. However, if you decide to give the details of your past kitchen work from 2008, there's a chance that the CO just might contact the person named - there would need to be someone there at the contact details given who would know about you and be prepared to confirm what you said you had done for that employer.