Nah, that's crazy. I think Beryl was just Beryl the last few pages. Nothing out of the ordinary and her whole behaviour fits with what is shown in the comic and what we know from her character sheet.
Also, I don't think Tempo has the ability or need to hijack Beryl to touch Alex. She could just show/feign friendly curiosity and he'd likely allow it. Especially now Alex revealed how easy humaniti males are with "handshakes". I'd like to remind everybody that
Beryl is canonically the spotty nerd with poor grasp of social norms to
Tempos physical perfection and impecable grasp of social poise.
Beryls suspicious slumber is well in line with her character flaw of falling asleep anywhere and the flow of conversation lends itself to that happening quite well also. Beryl was
awake and participating at the beginning of Tempos exposition. That's all ancient history for Beryl. She knows every detail already with her eidetic memory. Add to that, that she just spent an hour or so
milking Alex for new, exciting, alien metrics. Something she'd be far more interested (xenophilia) and therefore invested in. That takes its toll.
We likely haven't seen much of Tempo because a) she's tired as well and b) has her seatbelt on while the shuttle dodges Umiak divisions.
She may very well be able to mindcontrol others, but a fellow Loroi aware of such methods and trained in some manner of resistance, while Tempo is wearing no (visible) amplifier?
I'm honestly amazed how Tempo, the one Loroi most human is seen as this eldritch horror out of lies and deceit.
Here's my suggestion on what happened:
Alex is to be moved. Beryl and Fireblade get the order and pick up Jardin. While that happens Tempo gets told by Stillstorm to get lost too. Who knows, maybe Tempos behaviour on the bridge wasn't in fact technically not illegal. So suddenly Tempo appears on the shuttle, distressed and anxious. We know pretty well that Beryl is dumbfounded by Tempos appearance in the beginning.
Maybe the gesture from page 112 was the first moment Tempo had for herself to realise she's being sent off on a shuttle away from her actual post with some very strong words.
And just to be clear, I absolutely believe that Tempo has ulteriour motives with Alex and that she is to some extent deceitful. I just don't see her being this aggressive in her trickery (yet).