No the player should stay put during the cutscenes, and it is one of the many bugs. All rooms have this problem and I discovered this just after submitting the game. So to squash all these bugs and improve the interface I joined another jam, awaiting the results of this jam (and playing as much of the games submitted in this jam).
You can check progress here. Improve my Game Jam
Somewhere, if allowed I will add a more bugfree release.
And I had planned to add a ‘Wargames’ kind of room where a Matthew Brodderick lookalike kids plays the game with W.O.P.R. where the Star Wars satellite is used in the game and wreaks havoc among all communication sats in low orbit. But I had to cut these due to time constraints and ended up with one room and multiple cutscenes.