Analysis:Space-Time Transfer Device

Only When "That Guy" is Present
I'll give the conclusion first -

The Y-axis was bent when the player descended.

Since the player is able to freely move along the time axis, was the Y axis bent during the time jumps? Absolutely.

The main cause may have been in Kokoro's route. Kokoro made us believe that the events in the cabin and SPHIA occur at the same time.

The space-time transfer device may have been built to use a "god" (from Sunglass' perspective) such ourselves.

Random Transfer Phenomenon?
Moving slightly away from the Y-axis issue, let's discuss the the seemingly random transfers. When everyone is in their respective body, there's no way to tell when the first transfer will occur. However, there seems to be a trend:

Just before Kokoro or Satoru transfer, Inubushi becomes extremely agitated. When Kokoro reads the future newspaper, when Satoru blames Inubushi for the rat, when Yomogi and the others wish for help to arrive early -

Its seems most of the transfers are influenced by the character's mental state. The player, being affected by the tension, may inadvertently initiate the transfer.

33 Minute Rule
The first transfer occurs at random, but the next two transfers occur after 33 minutes. Once everyone returns to their respective bodies, the cycle repeats.

But why 33 minutes? The 33 minute rule may have been created by chance and Satoru's belief.

On the first day of transfers, while Kokoro is in SPHIA and Satoru is in the cabin, they experience the same random transfer duration (the fact that it was 33 minutes was mere coincidence).

On the second day, Satoru sees the 33 minute gap. and the player becomes convinced that it's some sort of rule.

Summary

 * Time is warped by the player, who believes both events are happening simultaneously at the start of Kokoro's route.
 * Transfers are initiated randomly, but it happens when characters are experiencing strong emotions. The player is affected by the tension.
 * The 33 minute rule when everyone is out of their respective body may have been coincidence, but the player solidified it as a rule.