Tube valve stem locknuts?

[twilliams]

I installed a new tube and tire last night and on the new tube there was a locknut and washer, without looking at the old tube I took off the nut left the washer on the stem and installed the tube then put the lock nut on. After getting it all installed I looked at the old tube and it had a second lock nut installed, so the old tube had the rim "sandwiched" between two locknuts, on my new one I have the rim "sandwiched" between the washer and a locknut.

The question is do I need to break the tire down again and put the second locknut on the inside?

Hope this makes sense.