It looked like Jon Snow was in charge at Dragonstone. Tyrion and Danaerys wasn't there and didn't see Varys himself. Missandei was there, but Jon Snow received Theon and proceeded to berate him and tell him the Queen is not there. Sure does look like he is in charge of Dragonstone when Queen and her small council was away. Either he bent the knee or he married her.
My interpretation was that him, Davos and Missandrei saw him and considering that Jon knows him, he was the first to speak. In addition, he is the only Westerosi (together with Davos) in that island. Daenerys' small council now contains only Tyrion (who was with her), Gray Worm (on the Rock), Missandrei and Varys (no idea where he was, but he never takes the lead in these cases).
Not sure how Jaime is the Aegon of books.
It has long been speculated, that before the War of Ice and Fire, there will be an another Dance of Dragons for the Iron Throne between Daenerys and Aegon. Next to Tyrells, Aegon has the biggest army in Westeros (Dorne + Golden Company) in addition to one of the top three commanders (JonCon is probably as good as Tarly and Stannis). If Tyrells declare for Daenerys in the book (because, why not), then we can expect Aegon to defeat them, before the clash with Daenerys. Well, in the show, Jaime defeated Tyrells and isolated Unsullied, making him Daenerys' primary antagonist. It has also been speculated that Dorne might kill a dragon (considering that they already have done it once), and Bronn' almost killed Drogon. And finally, people are convinced that Aegon is gonna get burned/eaten by Drogon, and that almost happened with Jaime today.
Jaime in the books probably will have a more minor role, if he survives Lady Stoneheart. Either join Brotherhood, or kill Cersei, but regardless, Lannisters aren't a big power by the end of sixth book, so a large scale between them and Daenerys isn't going to happen.
Obviously, it isn't a straightforward merge (like Euron/Vivtarion), but we can expect most of the fighting Jaime is doing, to be done by Aegon in the books.