"Although I did not go to bed yesterday, I am not tired."
Translation:Dün yatmamama rağmen yorgun değilim.
Well, if we reword this in a way that sounds really strange in English, it might help. "yatma" is actually a noun/gerund form (meaning there is no tense). So, this sentence is like saying "despite my not laying down yesterday, I am not tired." Notice, there is no need for the past tense here...Turkish uses a construction like this while using "despite." :)
rağmen is a postposition in Turkish a bit like how "despite" is a preposition in English - so just like preposition always come right before the thing they modify, postposition always come right after it.
You can't say "My going to bed despite" in English; it has to be "Despite my going to bed".
And so in Turkish, the rağmen has to be after the yatmamama and not anywhere else in the sentence.
I think the stress is usually on the last syllable in Turkish, although there are exceptions. This https://www.diu.edu/documents/gialens/Vol9-1/Woodard-Turkish.pdf paper explains the stress rules in detail. I don't trust Duolingo for accurate stress placement because I've noticed a lot of incorrect stress placements in the Spanish Duolingo.