Quote:
but Miyu demanded that she helped with security
I think you mean 'demanded that she help' here.
While I do not put it past the Professor to have built a useful time machine *. The way that this line reads is that Miyu wanted Ryoko to go back to an earlier point in time and help out with security, instead she is providing help with security now.
*And by Useful I mean the time machine has a temporal range greater than the length of time it takes to set up and activate.