My hamstring flexibility has improved so much, that today for the first time in my life, while doing Romanian Deadlifts the plates kept touching the floor.

Yeah yeah I know, cool story bro.
I think you are confusing negatives and eccentrics.

Negatives is a type of training method. When doing negatives, generally you do not do the concentric at all, or use very minimal effort for the concentric portion. For example, when doing negative chin ups, you jump up to the top position, and lower yourself down, you don't do the concentric portion at all.

Eccentric simply refers to the part where you lower the weights. In a squat and deadlift, that would be the part where you are going down, or in a bench press its when you lower the bar.

In terms of hypertrophy, during the eccentric portion is when muscles suffer microtrauma, which ultimately makes them grow. I remember Charles Poliquin once said perhaps instead of saying 'Hey dude Im going to the gym to lift weights and grow' we should say 'Hey dude Im going to the gym to lower some weights and grow'. Charles Poliquin and Ian King are the main proponents of slow eccentric lifting. They didn't invent it, but they were the ones who made it popular.

Sticking to hypertrophy, Poliquin suggests that in order for hypertrophy to occur, a muscle generally needs to have Time Under Tension (TUT) of at least 40 seconds. Imagine yourself doing bicep curls, if you take 1 second to lift the weight and 1 second to lower it for 10 reps, you'll get around 20-25 seconds of TUT, which is not optimal for hypertrophy. If you take 1 second to lift and 3 seconds to lower, that gives you at least 40 seconds of TUT.

In terms of strength, I'm not really very sure how to explain this, but I'll try my best. Basically, your muscles can lower more than they can lift. So there is a gap between eccentric and concentric strength. Your concentric strength will always try to catch up to the eccentric, which is why when someone who cannot do a single chin up starts doing negatives, suddenly he can do chinups, because his concentric strength is trying to catch up to his eccentric strength. If you constantly lift without slowing down your eccentric, there may come a point in time where your concentric strength doesn't need to catch up with the eccentric, and that's when you stall.

Using myself as an example, I implemented slow eccentrics less than 2 months ago. The first month, I did 10-12 reps at 4010 tempo (basically 4 seconds to lower the weight, no pause at the bottom, 1 second to lift, no pause at the top). It worked very well for hypertrophy. In the second month, I'm training at 4-6 reps, same tempo, and sometimes I'm shocked. I can easily increase the weight in almost every exercise, week after week. During the 1st month, I increased the reps, so if last week I did X weight for 10 reps, I try to get 11 or 12 the following week. During the 2nd month, the focus was on increasing the weight used. Progress has been consistent so far, hopefully it goes on like this.

Anyway, the main reason this slow eccentrics training is not popular is because you have to swallow your ego. You have to reduce the amount of weight you use. A lot of people say 'Well many people train without slow eccentrics and they're big and strong'. Yes that may be true, but that completely misses the point. Nobody is saying YOU MUST DO SLOW ECCENTRICS TO BECOME BIG AND STRONG. Slow eccentrics can allow you to have more hypertrophy and gain more strength, but I think the biggest advantage of slow eccentrics is that it makes it much more harder to stall, and stalling can be very frustrating.

Hope this helps you.