I recently bought a KTM Adventure 390. When I start the bike in neutral and then shift to first gear, the bike moves(jerks) forward a little, even though the clutch lever is still pulled all the way. Is this normal?
This is common among all motorcycles that have a "wet" clutch system. What that means is that the clutch is surrounded by fluid, usually engine oil. Even though you have the clutch pulled in which disconnects the clutch plates, there is still oil surrounding both the input and the output parts of the clutch. So there is some rotation from the engine being transferred to the input shaft of the transmission gears and this causes the "jump" you experience when you go from N to 1st. The technical term for this effect is called "viscous coupling".
Motorcycles that have a "dry" clutch such as some Ducati models, don't do this as there is just air which doesn't transfer enough rotational force to create the same effect.
Bottom line is that this is entirely normal and it's not a problem that needs to be corrected.
This could also be due to a loose clutch cable. On some motorcycles, there is also an adjuster found where the cable connects to the clutch and you might need to tighten the cable there. This shouldn't impact the clutch lever too much.