So what I've noticed is that depending on the internet connection, the time between buttons changing colors when you do actions fluctuates. On a super fast connection, I can fish pretty quick. However, when I switched over to wifi on my desktop (considerably slower), I started seeing a huge delay(an extra 1-2 seconds and with a game like this, it adds up quick). Is it a bug or is it all just dependent on how the game is coded?

Well, keep in mind that this entire site is exactly that, just a website. So like with any other website, the speed of your internet is going to affect the speed at which you load pages (thus, actions in the game).