Wait so I need to pay 0.02 BTC more to get to the minimum 0.08 BTC requirement for an address with 8 specified characters? I wish I was notified first. Please clarify before I deposit such an amount.
If the pool says the minimal fee is 0.01, then you need to send 0.01 to get the address into the public pool to be solved. Anything after that is a guideline - the more you pay the faster the miners will get to your work. Honest fee is an amount that would be fair to the miners in comparison to them mining blocks.
As I see from your link, your work is public, meaning that the miners can work on it and claim the reward.