First Contact from the Aliens' Point of View - How would you do it?

So lately I've been having sci-fi story ideas again, and I'm really into the First Contact scenario right now, since there's hundreds of possible stories you can get out of it.

The story idea I have right now is that one race of aliens is observing another race of aliens - the first race has space-age tech like FTL-capable spaceships, the usual stuff; the second has reached a medieval or possibly early renaissance level of development, akin to a Medieval European Fantasy setting (not exactly the same, of course, due to the fact that it's not Earth, but it's close enough; they have invented a printing press, at least).

It just so happens that Psychic Powers are a thing in this setting, and someone on this planet managed to develop a primitive device capable of channeling psychic powers into a powerful beam, and then accidentally shot down an observation satellite orbiting the planet. Soldiers from the local kingdom find the remains of the satellite and the queen decides to cover it up, not knowing what the hell it is, and she'd rather the populace didn't know, lest they work themselves up into an existentialist frenzy.

Meanwhile, the first race naturally find out about their destroyed satellite and the rudimentary psi-tech device used to destroy it; at first, their objective is simply to recover the satellite and either steal or disable the device, but things get complicated and they discover that doing these things without revealing themselves to the locals is, while not impossible, probably a lot more trouble than it's worth.

So what I want to know is: from the point of view of the observing aliens, what would be the best way to make first contact while causing the least amount of panic or fuss among the locals? The last thing they want is for some local fringe religion to declare them deceivers summoned from hell and chase them off the planet with Torches and Pitchforks.

Edited by PresidentStalkeyes on Oct 28th 2020 at 12:30:02 PM

Since neither of these species are humans, how they react to one another will be determined by the unique differences in behavior and attitudes between each group and the readers (who, I assume, will be human). So, we need to know more about the psychological characteristics of each species. How are they different from each other and from us?