Good god, FFS.
You are AGAIN actively giving out misinformation, so for the sake of the new person just trying to figure what is happening, I will go out of my comfort zone and attempt to explain this in a straightforward fashion.
This has nothing to do with FPS, and it has nothing to do with a person's ISP, or connection to the server. Your internet connection does not affect your FPS, or vice versa, they are two entirely different things that do not, and cannot interact with each other. That doesn't make any sense. It is the nature of FFXIV, and the MP ticks. The server will tick for MP regen every 3 seconds, you don't notice this in Astral Fire because your MP regeneration is disabled, and you don't really notice it too much in Umbral Ice because the MP gained is massive so it doesn't really affect your casts at your current level. When your MP goes to 0, if you transpose right after a server tick, you will sit at 0, in Umbral Ice, until the next server tick happens(~2 seconds if you're unlucky). This is why sometimes you will Transpose and immediately gain the MP required to start casting, because it means you Transposed right before the MP server tick happened. You can test this for yourself by Flaring a dummy, transposing immediately, and setting a 3 second metronome when you gain MP. It's very consistent.
I will attach a video to this comment that should give you a visual demonstration of what is happening on BLM specifically at this timecode, maybe it will make things easier to understand. https://youtu.be/id9aQ9sFptg?t=435
Getting into a cutscene, as far as I remember, will not remove or freeze buffs acquired, so during the cut scene, if you ended a fight with Despair or Flare, you are throwing yourself into Astral Fire, have no MP regen, but the Astral Fire timer will tick down DURING the cutscene, which is why you have nothing going out of it except for a paltry amount of MP, depending on how long you were trapped in there for.
BLM is historically an awful leveling experience for this, and similar reasons. There is jank in the early kits that will be ironed out as you level. In particular, when you get Blizzard IV at 58, you will get Umbral Hearts that will drop the cost of Flares and other Fire moves, keeping you above 0 MP for longer, Aspect Mastery at 72 which will effectively make the cost of casting spells of the opposite element free (ie Umbral Ice > Fire III or Astral Fire > Blizzard III), enabling 0 MP casts after Astral Fire dumping, and Umbral Soul at 76, which will refresh (but not apply) Enochian, grant Umbral Ice stacks, and grant Umbral Hearts, meaning you can keep up Enochian through downtime without the need to use Transpose nearly as often, if ever, so stick with it, it will get much better.
If someone can explain this better, and actually frequently plays BLM, feel free to correct me. Something very similar happens on DRK, so I'm familiar with the nature of MP acquisition and consumption sometimes having unusual interactions.