Doesn't "Tu aurais vu" mean "You would have seen" and "Tu aurais dù voir mean you should have seen

Yes, I agree with you. 

Normally, yes, but I think John is talking about this example from the lesson:

Tu aurais vu sa tête quand je suis apparu devant lui !

You should have seen his face when I appeared in front of him!

In this case, "should have" does not mean "you ought to have", so using devoir would be an anglicism. The meaning is more like "if you had seen his face!".  

In French, this could be either:

Si tu avais vu sa tête  or

Tu aurais vu sa tête (using the conditional instead of si)