Are my gears setup backwards?
No, it's set up the right way.  (In fact, because of the way the front and rear gear systems work, it's essentially impossible to set them up backwards: you'd have to re-engineer the whole system.)

Think about it in terms of how many times the wheels turn for each turn of the pedals. When you change to a larger-sized cog at the front, the chain moves farther for each turn of the pedals, so the rear wheel turns more times.  When you change to a smaller-sized cog at the back, moving the chain the same distance causes the wheels to turn a greater number of times.  So, in both cases, moving to a higher-numbered gear causes the wheels to rotate more times for each turn of the pedals.