尽管 and 不管 — two words that look alike

The rule 尽管 A，还是/但是 B = although A (a FACT), still B. Like 虽然, but more written.
尽管下着大雨，他还是来了。
不管 A，都/也 B = whatever A turns out to be. A must be left OPEN.
不管你说什么，我都不同意。
So 尽管你说什么 is WRONG, and so is 不管下着大雨。
尽管 has a second life as go ahead and: 有问题尽管问。