New to the diesel game - bought an '06 Dodge 5.9L Cummins to pull the 5th wheel - and so far it's been awesome coming from the gas engine world.
Have noticed - that if I slow down and make a turn into say, a parking lot, if don't downshift and stay in 3rd gear (6 spd. manual tranny) - the engine tends to speed up and pull me around the corner without any input from the accelerator - is this normal? Just thinking it may cause me some issues during our winter months and icy roads.  

computer is telling truck to speed up so it doesnt kill or lug motor. shift into lower gear.  

It is normal. You can let it idle in 6th gear and the engine will still push your truck around. And when you say 3rd do you mean 2nd not counting low or 3rd not counting low?