In this poem, Kipling is advising the United States about the likely consequences of their colonization of the Philippines. He is encouraging them to become an imperial power but is also warning them about the pitfalls inherent in doing so.
One of the pitfalls is that the "new-caught sullen people" will not appreciate what the imperial power has done. The colonized people will hate the colonizers. This can be seen most clearly in the lines in which Kipling says that the reward of the imperial power is
The blame of those ye better,
The hate of those ye guard--
Kipling also implies that the colonized people will repay their colonizers by destroying what the colonizers are trying to accomplish. The Americans will work hard to improve (in this case) the Filipinos but will get nothing for it. They will think they are finally achieving their goals, but then they wil have to
Watch sloth and heathen Folly
Bring all your hopes to nought.
Kipling is warning, then, that imperialism is a thankless thing. He is saying that the efforts of the Americans will tend to be destroyed by the people who they colonize. In addition, those people will never thank them for what they do and will instead hate them.
One can argue that Kipling's prophecy came true in the early 1990s when rising Filipino nationalism and anti-US feeling caused the Filipino government to eject US forces from bases in the Philippines.