Don't have any evidence of any job offer or work contract on you, and you'll be fine.
As far as immigration are concerned at Auckland airport, you're visiting to look for work. You're on another recce trip to confirm where you want to live, and have more interviews lined up.
If they grill you, you can say you have an EOI in, but as long as you don't mention the job offer (in which case they'd be expecting you to have a work visa/permit), you'll be golden. So if you have no evidence of it on you (you can pick it up from HR when you get here, then if you want I can show you where NZIS is in town), there's nothing they can prove.