I've got some IncaCoins that are close to 35 days old and my wallet is unlocked for staking...
When they hit the 35 day mark will I get an interest payment or does it take an additional 35 days once they begin staking?
Right now it says they are not staking because they are not "mature" yet  

Hello,  your coins will try to stake once they have their first 35 days (soon for you), 
Depend of the amount and the network, low amount can take few days more (but not much and no worries if it take more time to stake, you receive a little more too 

 )
Once your coins have got stake, they will stake again in 35 days.