Correct me if I am wrong,
running it off the oil pump gives you variable oil/gas mixture, as rpms increase oil increases though the pull of throttle so this will prolly save you money. However, if the plastic drive breaks your going to be running straight gas,so no lubrication.
If you premix its safer dont have to worry about the pump failing, but if you fill up on the water or top the tank off you need to figure out how much oil to put in.
my advice do what you want and works best for you. weigh the pros and cons for your self.