This particular point can actually be different depending on optional small talk, actually (or is addressed entirely, depending on your outlook on such things).
Should you return to the Source after meeting Feo Ul, Tataru's dialogue does change to indicate she's met Feo Ul and that you should go back to the First and let her worry about the Source. The quest in question, "Travelers of Norvrandt" actually changes a multitude of small talks! The Scions have kept many of their allies in the loop regarding the missing Scions, it seems.
Tataru, Matoya, Lambertient and Arenvald all change after this; Lamberteint doesn't quite believe the Scions are in another world, Arenvald worries for Alphinaud, and Matoya asks us to tell Shtola to come visit when she returns.(I do wonder why they've been updating Lambertient since 4.4...) Of those four people, three of them have the same small talk after completing 5.0's MSQ—Tataru's dialogue, however changes. For clarity's sake, here are Tataru's 3 states:
Admittedly, I learned this after I'd personally completed Shadowbringers by way of poking around GarlandTools and the like—but I do have a vague memory of checking in on the Rising Stones before Amaurot to see what, if any, diaogue changed and was amused/happy to see at least Tataru's did while the other Scions in the Stones didn't.
Another somewhat fun fact, is that the only other time dialogue on the Source changes is after you slay your first Lightwarden, Temulun (Cirina's grandmother) changes her small talk to the following:
Everyone else on the Source, other than those I've mentioned here, just seem to have a flag for whether or not you've completed relevant quests (the lv80 job quests) or Shadowbringers (the more mundane Scions). The citizens of the First seem to have a multitude of states, typically dealing with whether you've restored night to the area they reside in, if the Light's come back, and if it's Lakeland or the Crystarium there's even more nuance... it's honestly surprising and I'm ashamed to say I missed most of the interim steps!