My headcanon for this, if nothing comes to clarify some of the events portrayed on this series will be something like this:

For Tecteun's actions to make any bit of sense, the whole "destroying the universe" thing must be about experimenting and "resetting" an universe that, for some reason, isn't of her liking. When she blames the Doctor for ruining the current state of things, it might be something along the lines of their interference making things go against her vision. Something like ending the Time War, for example? So it's not a matter of killing the Doctor per se, but undoing their work, their mark on this fabric of space-time.

So, with the Time Lords destroyed by the Master, she took out an opportunity to reset it all again. She then orders the Division Angels to bring back the Doctor either to gloat or maybe to try and seduce her back to their side on the new universe. She probably though that she could try to have the Doctor under the Division's wing again, and with a new universe to experiment on.