I'm from Colombia and I understand the different cultures (yes, plural) and lingo there. Tumbao (tumbe/tumbado) is a slang expression that means deceive/rob/scam and I just say robbed. It also refers to a way of walking, with a certain sway for women and a "you know I'm cool" for men. Last but not least, it is said of a person that conquers or "gets", wins the heart of another (it applies equally to both sexes). In your text, it says "Tumbao es que yo soy importante" there, it refers to the way he/she walks. "Move over, I'm cool" sort of. However, below it describes the person that is lawless and makes no secret of his/her way of life and glorifies in it and so this reflects in his way of walking.
Bottom line, I'd say we go back to the way of walking that reflects his/her underworld way of life. And so, I go back to the "I'm cool" because it sums it all up. It's a way of life in a world of "it's you or me", a world that allows no other.