I don't bake with mixes, but I think you have 2 issues:
Extreme browning comes from a the high sugar content in your batter. Box mixes already have a high sugar content, but if you are using an extended mix you are adding even more sugar, which crystallizes and make a very crusty crust. Think creme brulee.
In scratch cakes, we deal with baker's percentages in our recipes (even if you don't know what that is, the recipe you are using follows it). I get a very light crust on my white cakes because the weight of my sugar does not exceed the weight of my flour so it is in perfect balance.
I am not sure if this is possible to get using a box mix, but here's my advice...
The second issue I think you have is it does not sound like you have introduced any moisture in your oven. Your top crust is cooking, crystallizing and setting before your cake comes close to being done. The longer it cooks, the more brown it gets. 2 things to combat this. Use bake even strips. Leave them dripping wet. But also try putting a 1/2 sheet pan 1/2 filled with water on the bottom rack of your oven and let it preheat and leave it in there while your cakes cook (and you will probably have to adjust your temperature up to 350 because of how much is on your oven). It will release steam introducing water to keep the surface of your cake moist. It should help it rise better, keep the dome minimal and it will slow how quickly it browns (if it domes at all it should fall when you take it out of the oven making the cake nice and flat). You need to re-adjust what you think "looks" done though, don't trust your sight or even touch since the top of the cake will me more moist then you are used to.