Define complexity. Maybe you can say that a mathematical equation is more complex if it has more operations in it. Does that make 1+4-2+8+20-1=30 more complex than 8x^2 + 5x + 4 = 26? You can always simplify complex things into less complex concepts, while on the other hand there is always more and more to understand about what--at face value--is as simple as a piece of bread. The bread is made up a complex netting made up of compounds made up of atoms made of up quarks... And complexity doesn't necessarily call for higher-order thinking processes, as you can make a complex program with 999 lines of code that can only do 1+1=2, while you can also make a program with maybe 20 lines of code that can do any operation with integers.
So, my first gripe is that we're throwing a meaningless adjective around.
Now, it's great that we can directly interact with the universe, but can we interact with the whole universe as it is? We can interact with the environment around us, but even then, we cannot comprehend everything. Is our current universe not already too complex for us? Therefore, if the universe became more complex, then maybe it is so that we would not be able to "handle it" with our brains, but how are you so sure that it'll affect us? If someone on the other side of the world from where you live is born, that most likely doesn't affect your ability to interact with those around you. With the same reasoning, if something outside of the environment around us became more complex, then it wouldn't affect us. In addition, since we do not currently comprehend the universe, how do you know that the complexity of the universe is what directly causes the complexity of our minds? How can you have such faith on the capabilities of evolution, that our line of species evolved to understand the universe by creating a brain with enough complexity? And the human species, like all species, is extremely recent. How can we say that during all these years in this universe all the species have maintained a complexity that scales with the complexity of our universe, a complexity that no other organism in any other universe has reached/passed unless their universe is around the same complexity?
So there is little chance that complexity of the universe affects the complexity of the mind, and complexity of the mind of "intelligent" life is always changing/increasing...At any point in time, the organisms in two universes may be in different "stages" of evolution, so evolution goes against this idea.