Where were all these assassinations before the 1930s?
I'd argue personally that the military always was capable of exerting this level of influence in Japan, but that up until the 1930s, the aims of politicians and the military always ended up coinciding (I wouldn't argue that they coincided perfectly, and by the 1930s, this was especially clear). AFAICS, politicians generally tended to favor good relations with the West and limited expansionism and imperialism, whereas the military favored major expansionism and imperialism, and in particular, were far more militantly nationalist. When expansionism involved fighting powers whom the "powers that mattered," ie, Britain and the United States, were either hostile or indifferent towards, such as Russia or China, over Korea and Taiwan, then the politicians could get their reasonably good relations with the West, and the military could get their expansionism. During WWI, Japan could take the German concessions and colonies in the Pacific and even manage to get brownie points with the UK and US at the same time.
By the Taisho period, however, the areas of potential expansion are drying up, as Japan now has Korea, large concessions in China, and influence or control over a large portion of the former German concessions. If Japan were to expand further, as the military wanted, they'd have to make completely intolerable demands in China, most of which proceeded to manifest themselves in the Manchurian crisis, and eventually the Second Sino-Japanese war. Likewise, if they were to continue expanding past Taiwan and the South Pacific Mandate, they would come into inevitable conflict with the USA, the Netherlands, and the UK. Further aggrandization in China was also likely to trouble the USA and the UK, as the theoretical end point of a China (or even just Eastern China, which is the most valuable portion anyways) totally dominated by Japan was extremely unpalatable to the USA and the UK. I think to some extent, those who feared Japan saw China's position as Korea writ large, with Japan steadily taking over the institutions, and exercising a larger say, until the country was a de-facto colony, and possibly, province (Japan probably could not have annexed and turned into a colony the whole of China, as they did with Korea, but even a string of puppet states was more than worrying enough).
So basically, you have a fundamental disagreement between the politicians, who see a need to maintain good relations with the West so as not to worry them with their continued expansionism, and tamp down the military's budget, so as to limit their influence on government, while at the same time, the military wants to damn relations with the West and expel the Anglo-Saxons from the Pacific. By the 1930s, their views are completely divergent, which leads to the "assassination politics" and militarism that characterized the Showa era. By the mid-1930s, the military are even daring to violate the person of Saionji Kinmochi,who most favored limiting the military, and was perhaps the most influential politician in Japan at the time.
I don't think you can have actual "cut-off" points for when Japan specifically turns from modernization to liberalism to militarism; though the Meiji, Taisho, and Showa periods tend to coincidentally line up with those eras pretty well. Nationalism, Imperialism, and Liberalism were already major factors in Japan during the Meiji Era, though much of that era was concerned with modernizing Japan to the level where it could hope to match the traditional European Great Powers, let alone become a true Imperial Power. Likewise, by the late Taisho Era, you can easily see the cracks beginning to form in Japanese democracy, such as the rejection of the eight-eight program by the Diet, and the signing of the Washington Naval Treaty, which was detested by the militarists, and which showed that the interests of the militarists did not at all coincide with the interests of many politicians (also of note is that many of the laws which permitted the Showa dictatorship were first promulgated under the "liberal" Taisho era). A lot of aspects of the Showa era, such as the belief in a Japanese "master race" destined to rule Asia have roots which predate even the Meiji Era. There were always politicians as insanely nationalist as military officers, and some surprisingly liberal generals. But generally, I don't think it's wrong to say that the Meiji Era was defined by modernization (and westernization), the Taisho era by both liberalism and expansionism, and the Showa era by racism, ultra-nationalism, the trampling of democracy, and fascistic militarism.