I NEED HELP- Difficult beat and rhyme scheme

[xJPx]

Ok hopefully someone can help me here. I'm learning how to rap. I already watched videos on the basics of counting beats, understanding bars, making rhymes, etc. I'm having trouble with one specific beat and a rappers rhyme scheme on that beat.

 

The beat is the old town road instrumental, You can listen to it here. Its 136 beats per minute. The beat drops around 27 seconds. I've counted the beats myself to the instrumental to see if I'm doing it right, and I am. I roughly count 68 beats in 30 seconds, which falls in line with 136 bpm. For some reason though, when I am rapping on this beat, it doesnt feel natural nor right to start rapping right on the first beat. I feel like I almost need to get a rolling start and start before the first beat for it to sound correct. If I wait until I hear the first beat to start rapping, I sound off beat. But if I start right before the first beat, it sounds right. A perfect example is this rapper Here. His name is shotty horroh. His first bar starts before the first beat drops. Why does this sound normal and better vs waiting until the first beat? Also, when I use a metronome, and/or count the beats as shotty is rapping (starting from the first beat), his lines are ending in the middle of the bars of the instrumental. Literally, start a metronome at 136 bpm right when the drums kick in in the background of this freestyle, and you'll notice his lines end in the middle of the instrumentals bars, if I'm counting this bars correctly. It isn't until a few lines in do his lines end on the 4 of every bar in the instrumental. The first 6 lines or so end on the 2-3 beats of every bar. 

 

Can someone explain this to me? Is this what hes doing? Why does it sound normal to start rapping before the beat drops on this instrumental?