True fact: the US was hardly better at ruling places like the Philippines than the Spanish were. To quote William J. Bryan: "All we did was replace an oppressive Spanish regime with an oppressive American regime."
If it had been German the Philippines would become a League of Nations mandate after WW1 and been given to either Britain (likely) or France to administer. Independence after WW2 as IRL. British rule probably less oppressive than American, French rule about the same. I doubt Britain would have accepted a Japanese conquest of the Philippines and the Japanese wouldn't have wanted to upset their alliance with Britain prior to WW1. If the Philippines had remained Spanish to after WW1 a Japanese attack on them would probably lead to war with US and Britain. Also the Japanese where busy in China and not ready for a war against the Western great powers in the 20s and 30s.
If Germany had obtained the Philippines the most likely result would have been that it would have been split after WWI into a northern mandate awarded to Japan and a southern mandate awarded to Britain. However, I think that if the United States had not annexed the Philippines outright, we would have gone for a Cuban-style quasi-independence, complete with a perpetual lease on Subic Bay.
