I can't speak for Vietnam. Here's what I do know. Sorry if it jumps around a bit. Feel free to ask for clarification on anything but the Philippines, for which I wouldn't be able to provide any.

China

In the late 1800s there was some pretty serious anti-Christian sentiment in China. This eventually became the Boxer Rebellion which in the end only led to more foreigners and more missionaries. It wasn't until the Communists came about that missionaries were really removed from the country. However before that, in terms of forcing, they didn't really have the ability to do so. They could entice you to learn about their religion, but not a while lot more.

However there were ways in which they would force you, in a sense, to do things like Bible study. In the early 1900s there were a great many missions in East China. I have some old teaching materials from one that existed in Changzhou and Suzhou. They actually began under the banner of teaching women how to do sewing and embroidery that could then be sold, helping to bring the women out of poverty as well as giving them something to do. These missions spent a great deal of time teaching the women how to read (based on a modified version of the national alphabet at the time). However, if you wanted to be a part of their embroidery classes, you also had to attend a bible study class. If you wanted to learn to read, well you ended up reading the Lord's Prayer and bible stories. So, not forcing, since you didn't have to benefit from their works. But if you did want to benefit from what they were doing, the payoff was learning about Christianity.

Korea

Similar to 1920's China, missionaries in Korea weren't really in a position to force you to convert. They came much later, following the Korean War. There were missionaries on the peninsula before this, but in smaller numbers. It wasn't really until reconstruction of the South after the ceasefire that they began to flood in. Their efforts were also similar to China in that they offered things like food and clothing in exchange to learning about the religion. They were much more successful in South Korea than they were in China. Today, of the people who consider themselves religious, over half are Christian.

Taiwan

The Dutch in the 1600s brought missionaries, but they were mostly unsuccessful. The Spanish as well, but with the same result. The most successful was in the 1800's with George Mackay, a protestant who developed the still-used romanisation system for the language, as well as setting up a network of hospitals that are still running today (albeit in newer buildings). However, despite seeing some converts, Taiwan is still less than 5% Christian today, with no major event causing the number to drop since the 1800s. So again, not terribly successful as far as conversions.

I'm actually going to step away from Christianity for a second, even though your question is strictly about Christianity, but the following is directly related. In Taiwan, there has been non-Christian mission work intentionally based on the model of Christian missions and their methods. In the 1960's in Taiwan there was a Buddhist charitable organisation founded named the Tzu Chi Foundation. Their model of charity is intentionally modelled on that of American Protestant missionaries. It's much the same idea as above: We come to you when your village is ruined by landslides, and we come with food and clothing, but it's at a cost. They have been widely criticised by the aboriginal population for their methods, as it was seen as a sort of extortion. You'll still hear these criticisms today.

Philippines

After the Spanish arrival conversion to Christianity saw a pretty big jump. Their practices were a little more extreme, because they had the power to do things like forced relocations and mass baptisms. However there wasn't much of "convert of we'll kill you" type of "mission work" going on, as far as I know. That's actually the extent of my knowledge on Christian missionaries in the Philippines, but maybe someone here knows more.