But Rolan's right, best way to take over a people is to switch who they're paying taxes to. If you lower them a tad and reduce the brutality of law enforcement, they'll welcome you with open arms often as not. That's why you need propaganda to keep them in line.
Take them over until the man paying you taxes turns into a horrific monster that eats off your face. That's the problem, though. Let's play a thought experiment.
Tau get stronger. They do this at the expense of the Imperium. They become dramatically stronger, and smash Imperial lines. The Imperium is weakened. Tau gains sway over a large number of Imperial worlds. Imperial lines on other fronts are stretched thin to combat Tau threat. Maybe they get within striking distance of Terra, why not. The point is there is a Hypersphere expansion or whatever you want to call it, and they push and push and don't stop. But, eventually, the Tau push too far, and the Imperium enters extended collapse. That means Orks, Eldar, all sorts of fun stuff starts getting !!FUN!!, but you want to know who takes advantage the most? Chaos. Boom, 14th Black Crusade, and with the Imperium outstretched EVEN MORE THEN BEFORE, Cadia falls for good. Now, what? Now the Eye of Terror starts expanding like crazy. The Imperium's collapse becomes a freefalll. The Tau don't see the trap yet, and do quite well in this period.
But here is where it gets bad. Maybe it's because the Emperor gets fewer Tithes, maybe the inevitable effect of the Golden Throne does it, maybe the strengthening of Chaos weakens it, maybe Chaos just straight up takes Terra, maybe all of these things; but either way the Warp becomes dramatically stronger (which it would even just because of Cadia falling), and the Emperor+Astronomican become weaker until they cease to exist. Now suddenly, the Tau's billions of human subjects start the clock on the end of the Tau. Because you see, the fate of humanity, a warp-sensitive, soon-to-be-fully-psychic species, is inextricably tied up with the fate of the Emperor and the rest of Humanity. If the Imperium is weakened to the point of free-fall, the support system that stops Chaos is weakened for ALL of humanity. If Tau pushes far enough, the Imperium can't defend itself. If the Imperium can't defend itself, EVERYONE gets stronger. If EVERYONE gets stronger, Chaos almost by definition benefits the most, since their plan to win is basically "conquer Terra, the entire Imperium is cut off from itself and helpless, new Eye of Terror consumes the galaxy, gg no re". All humans the galaxy over are dragged, often literally, into hell. This includes the humans on Tau worlds, which are full of ripe, undefended human souls.
Entire worlds scoured of life by demonic hordes. Demonic possessions doom billions. The scale of the chaos (and Chaos) in Tau space is beyond their comprehension. The Tau completely, utterly powerless to respond, or even understand, the nature of the threat. Billions die in weeks, maybe days. Above all, Tau don't understand what is going wrong. They don't get how things get so horrifically turned around; worlds that long ago embraced the Greater Good suddenly dropping everything in worship of strange gods. Sure, they can stop some threats, but ultimately they don't even have the tools to identify the risk factors. Humans do, so if the Tau are lucky they let their human pets revert to tried-and-true methods and begin witch-hunting of psykers, but every time one slips through billions suffer the consequenes. Tau are forced to call off any offensives to deal with the fact that worlds they thought they had pacified were suddenly literally vomiting up hell. It doesn't matter that they stop. Even if they pull back all the way to their homeworld, the Imperium is too fucked to save itself, and the Tau don't have the tools to handle it. If the Tau are smart, they start wiping out Humans en masse. If they do (which is a fairly tall order), they save the worlds that remain, but its a temporary victory.
Eventually the Last Black Crusade, taking its victory lap through Imperium space to convert ever more into demonic playgrounds, reaches the edge of Tau Space. Maybe the Tau are ready to negotiate. Maybe they don't. Maybe they simply doubt what they see. It literally doesn't matter. Chaos has already won, its just mopping up. Tau fight hard, but the sheer weight of it combined with their losses from rebellions and heresies means they are ultimately doomed. The Galaxy belongs to Chaos, and the gods make sure to erect a horrific, perverted monument to Chaos United, celebrating their triumph, on T'au to memorialize those who did so much to aid their victory.
TL;DR. Tau cannot win. They actually cannot ever win, because to win, even gloriously, demands that the Imperium lose. Most races, when they win, do something that ensures their victory, but even the most OP-plz-nerf tech the Tau come up with cannot match the Storm of Chaos empowered by the rotting husk of the Imperium because the T'au don't even recognize the Warp. Other races destroy the Imperium and (or just) empower themselves in a way that can beat Chaos, but Tau cannot ever beat Chaos on their own, and they can't understand how Humans do it (and regard it as insane religious dogma). Tau would be doomed by their success; in fact, the best possible outcome for them is that they DON'T expand into the Imperium, and just quietly tech-up until they either surpass the Imperium at its height or actually get souls like a real sentient race. But the Tau can't afford for the Imperium to collapse since its collapse will inevitably destroy the Tau, and since the Imperium is sure as hell not going to go down peacefully, collapse is the only option.
Tau expansion, at the VERY POSSIBLE BEST outcome, lead to the Tau finding themselves in their own Age of Strife, with the Imperium acting as the Fall of the Eldar analogue. It would even share a lot of the same characteristics, with various far-flung worlds falling to Chaos from Psykers they can't handle, only with aliens (humans) being the main driving force. That is the best possible outcome. They would inherit a Universe that hates them and everything they stand for, and they would have to adopt a strict "murder all shit that smells like Chaos" policy to survive for long. Of course, then, they are no better then the Imperium was for humanity. In fact, to even have a chance to survive at all the Tau pretty much HAVE to adopt a policy of vigorous apartheid at best and genocide at worst, because they will get fucked over heresy, chaos, and mutation. Hey, that sounds like what the Imperium does...
TL;DR: To beat the Imperium the Tau will become the Imperium, one way or another; whether they copy how the Imperium rules, or the part where they are dragged screaming into hell along with their human slaves because the Imperium wasn't just full of superstition to be closed-minded bigots, they were doing that because every other path leads to death. Even Eldar understand this, that's why they are so fucking rude all the damn time. The only options are to be the super open-minded psychically attuned race that can appreciate Chaos for what it is and reject it, or be ignorant and reject outright as unthinkable and heresy. The Tau though are so ignorant the close-minded path doesn't work, because close-minded only works if some people in the leadership can make it go away. Tau can't make the Chaos go away.