Is this leather veg tanned?
It looks to me like you're conflating the tanning with the dyeing processes:

Tanning vs Dyeing

Tanning is how you turn a piece of rawhide into leather - it does change the colour, but that's not the main purpose.

Dyeing is how you change the colour of an already tanned piece of leather. 

Telling Veg-tanned and Chrome-tanned leather apart

There are two main ways to check if a piece of leather is chrome or veg tanned. The first is stiffness - veg tanned leather is normally quite stiff, and can be impressed when dampened. 

The second is colour; undyed veg-tanned leather is a salmon-pink fleshy colour (like you have), whereas undyed chrome tanned leather is normally blueish-grey.

Your leather

Looking at your picture, it looks to me like a piece of veg-tanned leather that's been surface dyed rather than through dyed - the dye has been applied to the surface and hasn't had a chance to soak right the way through. This is quite normal for pieces of leather that were bought undyed and dyed at home.

Unless you have other reasons to be concerned, I'd say that the tanning is perfectly fine and you have nothing to be worried about there.

Yes, the dye will fade and rub off more quickly than if it were through-dyed, but you can always apply more dye if you need to. Applying some sort of leather finish such as dubbin should slow the fading.