I'm talking to Alvin from Avazu about joining their network. Their policy with payouts is $1,000 minimum. That means that I need to accrue at least $1,000 in payouts before I can withdraw any of it. Any future withdrawals must be at least $1,000 as well.
Is this normal/OK?
Pretty normal yeah.
Many networks have lower monthly minimums e.g. $250 min for a wire and most will want $1k/week before considering weeklies.
$1k is on the higher side for payout threshold but is small on the scale of the revenue many affiliates are pushing... hence why cash flow often holds you back as a newbie.
Maybe team up with another newbie or 2 at the start to hit the initial payment barrier 
That is a bit higher than the industry standard.
However if you are short on cash and need that to push more volume I would just ask them for an exception.
They are pretty reasonable and that would help both long-term.