Second, she establishes his diplomatic credentials in front of witnesses. Still-Storm might already have had a low esteem of him, but a move like this would nix any idea of hers to silently interrogate and get rid of him. Though I'm not quite sure on the 'interrogate' part since it seems they were all at the end of their wits when their telepathy failed.
Third, she's already seen limiting Alex's access ot information (http://www.well-of-souls.com/outsider/outsider065.html), so her plan might be to continue acting as a watchdog and a filter, to ensure others (especially Beryl) don't blab in his presence about things better left unsaid.
It might be a 'good elf, bad elf' routine on a different level. Here there is Tempo who actually came through with the promises she made (or at least it looks that way to Alex), then there is Still-Storm who wouldn't like better for him to get off the ship... or worse.
For Tempo, it would be a win-win situation: Were Alex to be an enemy spy/plant, she could misdirect him if needed, were he not, she could continue to establish bona fides and maybe pick him for some intel about humans. Beryl may do so as well, but she isn't trained to ask the right questions or in the right tone.
Yet, her posture in the last panel is something I find more curious, and I'd loved to see that scene in motion. She has her left hand lifted up to her ear, yet it doesn't look much like she's holding something in it. So it could be that either she's fiddling with some concealed device, akin to a bluetooth earplug, for whatever reason, or...
she was about to do something like raking her hand through her hair. Definitely possible, since we have already reason to believe that
- Loroi do have about the same range of expressions as humans. For example, they express mirth the same way humans do, by laughing.
- Tempo herself has undergone training in diplomacy and interrogation, and it would be safe to assume it includes a whole range of interpreting and using nonverbal expressions. As seen in http://www.well-of-souls.com/outsider/outsider066.html she does consciously intrude Alex's personal space, to coax a reaction out of him. (And in the following panel, one can see that it actually worked.)
Either case, she does seem to have her own agenda concerning Alex.
Or maybe a cigar is just a cigar. But when it comes to politics and intelligence, things rarely are what they seem to be on the first glance.