In general, I do approve of the way that the US handled these things (I assume that you are asking about the relationship between the US and Japan around the turn of the century, not the later relationship that led to the Pacific War). I do not know if the US acted for the right reasons, but I think its actions were reasonable.
The US wanted to be able to trade with China, but China had been carved up by European powers. These powers generally had areas in China that they controlled. The US wanted access to those areas and therefore proposed the idea of the “Open Door.” Whatever the US’s motive, the idea of the open door was a good one. The US involvement in the Boxer Rebellion was relatively benign as well. We surely cannot condemn the idea of sending troops to rescue Americans and Europeans trapped by the rebellion. We can take some pride in the fact that the US gave back some of the indemnity that China paid it. These were not dishonorable actions.
The US relationship with Japan at this time was handled relatively well too. The US did, in essence, split Asia up with the Japanese, recognizing their control of Korea in return for Japanese acceptance of American domination in the Philippines. This may seem imperialistic and cold-blooded, but it was very much in line with common practice at that time and, at any rate, we were certainly not going to fight Japan over Korea. In general, the US treated Japan fairly respectfully during this time.
For these reasons, I am inclined to approve of American actions towards China and Japan during this time period.