This Rin is a pseudo servant like Waver/Zhuge Liang and Matty/Galahad right?
Kinda but not quite. It is a Pseudo-Servant, yeah, but where Zhuge leaves the controls to Waver and Mashu is technically something else entirely (Demi-Servant, not quite the same thing), here it's pretty much Ishtar in Rin's body. Though let's be honest, the two are a lot alike so it's not that off-putting.
Babylon answered what's going on here. Essentially their summoners tried summoning Ishtar and needed a vessel. For whatever reason, they could grab a suitable vessel from any time period and it just so happened that the best was Rin.
So that's all. It's Ishtar with Rin's form. Ishtar herself says that there's no one else in there but her, but aspects of the body's original owner affects her. As she said, she's 70% Ishtar and 30% Rin. Gil admits that she's actually better like this since her personality has become less spoiled and rotten thanks to fusing "with a girl who lost her father at an early age".
