I hope others will offer advice as well.
Simply put, yes, finish the inside similar to the outside. Reason being, you want to equalize the movement of moisture in and out of the wood. If the inside were not finished the wood would take on more moisture on the unsealed inside of the box than it would on the outside, sealed portion of the box. This could lead to unwanted warping.
The pencil box is small so this might not be a problem, but better safe than sorry.
That said, you don’t need to add coloring on the inside if you don’t want to. Just the clear sealing finish throughout.
I’ll look forward to seeing your finished box posted in the My Carvings! forum!