From the lore book entry on the Hyperstellar Downconverter (pg 167):

...was developed to communicate with Dalamud...It was later repurposed and improved upon to facilitate communication over the massive distances between stars.
Now it's possible this was just a fun toy technology and they had no idea if it even worked. However, it seems plausible that the need for and practical testing of such a technology means the Allagan had a presence on a world other than our own. (or, to be a party pooper this could have just been used by Xande to communicate with The Cloud of Darkness).