I agree with the idea of stop paying them directly now, put money in savings so it's available to you if they ever do have a true financial emergency (which hopefully they won't), and in the meantime it's earning interest instead of being blown every month. If you take the approach of "paying them back" for rent for a year or two, I'm concerned you will wind up right back in the same place you are now - them expecting this money (and more!) from you every month, and you agonizing over what to do. It's best to just deal with it now, IMHO.
My husband and I aren't Asian, but he is the oldest of his 3 siblings, and he's like you in a lot of ways - got a degree (which he paid for himself through scholarships and student loans, which he paid off within a year of graduating), got a good paying job, we're very responsible with our money (no car payments, only $6k left on the credit cards from $150k in medical expenses over the last 12 years), I have a good paying job, too.
Meanwhile, his siblings (both in their 30s) don't work, still live at home, and his parents pay for their brand new cars (we drive a 1998 and a 2005, both of which we bought used and paid cash for), their clothes, their food. When the fiance (also unemployed and living with my in-laws) of one of the siblings complains that they didn't buy enough of his favorite soda that month, they run out to the store to buy more.
My in-laws are planning to retire next year. They still have a large mortgage, which they plan to continue having in retirement, and they only have the same amount saved in their retirement account that we do in ours, even though they're 30 years older than us. Thankfully they have pensions and 401ks that will help them, but it will still be tight.
My point is, in all likelihood they will continue to support their children until they die. (Any time we suggest that they recommend the siblings get a job, they say "We can't do that! That will upset them!" The siblings practice a lot of emotional blackmail - threaten to harm themselves if the in-laws ever suggest they take responsibility for themselves, but refuse to see a mental health counselor or other professionals for help.)
You don't want to wind up in the kind of situation where you're providing a large chunk (or all!) of the financial support for your parents and/or siblings for the rest of your life, and it's deceptively easy how guilt, expectations, and a strong desire to please the people you love can combine to make that happen.
In our case, we flat-out say to my in-laws every once in a while "You do realize that heaven forbid anything ever happens to you, we will not take over financially supporting the siblings, right?" Our 3-year-old already understands the concepts that 1) things require money to buy, 2) she will need to get a job to buy her own car and her own house when she is ready for those things. (She has decided on a red car already.) Our 1-year-old will also be taught those things at a very early age.
Please do keep us posted on what you decide to do.