Does the issue occur when you are shifting positions or when you extend your fingers?
If this happens in 1st position itself, try not to move your thumb, since (as you imply) it is a steady base from where you build up. If the issue happens when you come down from 3rd to 1st position, repeat the shift of the left hand, but play the same note to see what happens. (For example compare the A played with 1st finger on 3rd position on the E string, with the A that you play with your 3rd finger on the 1st position)

I suppose that the braille dots will immediately solve this 'symptom" but not the cause. The good news however is that you realise you are sharp so you can fix it with some exercises. Play the scale and try to find the exact part that your thumb moves out of position. Isolate that motion and try to repeat it correctly many times (it's nerve wrecking, I know, but it if you are patient it really pays off). Move and check the note, correct it if wrong and repeat. A piano/keyboard or a chromatic tuner could be of great help btw. 

Memorising the thumb's location is quite helpful, and resolves many issues. And of course it will be a great asset. There is a chance that after you put the dots you would completely rely on them not bothering to memorise where your thumb should be - without even realising it. That would be my only worry about the dots. 

Hope you are successful

Hermes