It's normal for it to change rapidly as you bring online more and more coal plants and other civs start doing the same, especially if there's much deforestation. Your example is a bit surprising to me though, since there was only 1 turn between the phases. In my current game I had 9 turns between phase 3 and phase 4. Also it's telling me that CO2 was adjusted by 30% due to deforestation levels. I'm not sure exactly what that means but I guess it could've been 30% less if not a single forest/jungle were chopped in the game.
Considering how you're a big fan of chopping
@Lily_Lancer I think you will find it a bigger issue than some other players since there is a big modifier with deforestation. But you're not the only one, I remember seeing some youtube vids or it might've been a comment somewhere that unless you beeline computers you have no chance of building flood barriers in time, but for me I manage to reach computers before climate effects even begin in most games. Then again, I take climate change into consideration while I'm playing. I try to switch from coal to oil asap and build renewables also asap. I read some discussions that coal plants are the best (for some reason I don't understand), so for those players it'll be a bigger issue. Again, if you play domination which a lot of players do, it's another contribution from military units that use coal onwards.
So yes, if you don't keep the climate in mind, and you do a lot of chopping early game, focus on coal plants, then I'm not surprised it'll suddenly increase in that way coinciding with the sudden burst of coal power plants combined with deforestation. Now that I think about it, during one of my first few games with GS I was in this type of situation where phase change was happening almost every 2 turns or so.