A simple way to put it, in addition to the answer given above, is that Le Chatelier's principle involves where equilibrium lies whereas rates involve how quickly equilibrium is reached, wherever that equilibrium may be. You're right - since this is an exothermic reaction, increasing the temperature will shift equilibrium towards the left. But that equilibrium will also be reached quicker - hence the increased rates.
Well, if you're just starting with all reactants, there will be a huge impetus for the system towards the equilibrium mixture of reactants and products. Since no product is present, the forward rate is extremely large. Since there's no product, there is no reverse rate. But once the system starts generating products, there will be a reverse rate. If there is only a little product, the system will still have a large forward rate and a smaller reverse rate because that's how it will reach the equilibrium distribution. In this way, the forward rate keeps decreasing and the reverse rate keeps increasing until equilibrium is reached.