Cal here from Shopify, thanks for reaching out to us. Congratulations on launching your store, and making your first sales! That's amazing.
Your payout schedule being set to every day does not necessarily mean that funds will be transferred daily to your account, it simply means that when there are funds that have cleared from your customers, it will be sent directly to your bank every day. There is a 'pay period' that you must consider which you can learn about here! It looks like New Zealand is on average 3 days to process funds.
Congratulations again on the great start to your business venture!
I would suggest having a look at each order timeline in Orders > Choose the order > Timeline, and you can see the gateway used and if it was a successful transaction! This will give you the best indicator that all was processed correctly.
If you see anything suspicious don't hesitate to reach back out here or get in touch with our live support team to have a look here.