I've made sure this is added to the tracker. Are there any specific steps that seem to reproduce this? Perhaps in the game setup.
Nothing in particular. I tend to play in immense maps with many custom races and ships from Steam Workshop.
It is really happening once you have discovered and established contacts with many races. Once your turn begins, sometimes, but not always, there are multiples races trying to contact you, and they seem to pop up one after the other without the user doing anything.
One appears, it is closed automatically, another one appears, it is also closed, another one appears and then you get a dialogue (or simply have to click "done"). Sometimes only two windows appears like that, somethimes 3 or 4.
This has been there since the beginning of the game. I can't replicate it, reloading a save game from the turn before will give something else (maybe no window, maybe only one dialogue window, etc).
Lots of people seem to be reporting this issue, we all have different setups.
You could try to play with this game until the issue reproduces, but it could take a lot of turns, it might even not happen at all 
In this game, I have also noticed that races I have already established contact with are using dialogue lines like it is the first time they see me. I've never seen something like that before, and I am wondering if it is my particular setup for this game, having one ally from the start, I "meet" races as my ally meets them, and then once more when a survey or scout ship encounters them (or they encounter me)... I haven't paid close attention to this particular problem, I was more focused on the multiple windows issue.
Anyway, here is a save you could try:
My save game
