[From David AKA Goruku, main game designer and time programming]
The original time travel idea comes from one of the solutions to the grandfather paradox with alternate timelines. Essentially any act of time travel creates a new pocket reality and you may never come back to your original reality (since coming back is itself a branch, it didn't happen the first time). This allows you to influence the timeline without influencing your own past, because that timeline's version of you is not YOUR past, thus the grandfather paradox is avoided.
In that framework, the possibilities are technically limitless, you can branch at any time anywhere, to any existing branch, and this becomes more of a logistical problem: you would have to keep the state of the world in memory at any time, every time, which is not sustainable.
This system has been a long-standing fascination of mine with time travel and I've been wanting to implement it for over 4 years, the fleshing out of the idea only happened earlier this year where thoughts about implementation limitation were conceptualized, although unfinished
A side solution is the system in 5D Chess with multiverse time-travel, but I personally dislike the movement between realities since in my interpretation that would branch too. I did hear about Quantum League and seen some gameplay, but I don't recall it being a source of inspiration for the pulse system itself (surely it may have influenced though), the replay of instructions was a side product of memory limitations, but it was mainly inspired from the replay system Blizzard Entertainments uses for their RTS, of all places. To save on replay size, and since their gameplay is entirely deterministic, they only save the world state at keyframes, and replay inputs all stored chronologically in a big text file. We have a similar system but are running concurrent replays (what you play is actually a live replay of your timeline)
The pulse system is born of a need to only save the state of the world at specific points in time, since doing it every single frame or fixed interval would be unsustainable. The benefit though is giving fully functional power to the player's jumping capability without compromising the time travel rules by limiting the jump window and scope, it also provides players agency and choice as to their usage and resource management through time.