
Well, the prince's behaviour was the same as in the past and it would have remained the same if Tia didn't show clearly she doesn't want to be with him.
Tia's "change of heart" changed the course of events, of course people and things are bound to change as well (Allendis and Carsein becoming famous earlier than in the past for example, or getting to know Tia too).
As for the famous girl, I think she's called Jieun, she was apparently a key person in the prince's hatred for Tia. If her appearance doesn't get anticipated like other events, she should appear in this world when Tia is 17. I don't remember how old is she now, but I think there are at least 2 years before Jieun's appearance.

imagine someone despice you envy you and even hate you to the point that he will kill you oneday without a deep investigation .....he will kill your familly confiscate all your proporities ! do you think coz you don't want to be with him can make change his heart? he will hate you even more becoz of your arrogance ! how dare you refuse a futur empror !and if he find that you fear him he will bully you even more ! reread the firsts chaps... it's illogical ! your words apply to doctor elise she refuse the crown prince but what she did for the empire is priceless, she is a treasure how he can escape falling for her , adore her like a godess !!!! ?

I don't know, there are a lot of plot holes in this story. What I mean is that since the future changed, people changed too.
For the prince's behaviour in the first chapters there was a reason I read somewhere here that doesn't make any sense AT ALL, but it is an explanation.
I think you're wrong in thinking that the prince has always been this horrible person whe knew at the start. People don't go on rampage for no reasons. There must be a reason for him to be this cruel toward Tia in the future we know. Here it's still a kid. Even thought people keep on comparing him and Tia, there's no reason for him to think of killing her or rape her, like he did "before". Never once in the present time he showed a behaviour that would lead to think he's going to treat Tia wrongly.
Plus, you say that if he knows she fears him, he'll bully her even more. I can't remember scenes where the prince is bullying her in this timeline, and I'm not going to reread this manhwa now, so my memories may be at fault. What I remember is a shocked prince that doesn't know what the hell happened between him and Tia for her to be this scared. And his only clue is a letter that speaks of events that never actually happened in this timeline.
I think I will droop this manga ...I don't like nor understand why and how the prince have changed !the FL changed after being killed ok ! but the prince change is illogical...he was jealous of her for ages being compared to her ...his reaction must be the opposite of what he is doing now...and the famous girl is nowhen to appear ...his soulmate the brown girl from another word ! she is supposite to be his bride How can god be mistaken .....?! Σ(  ̄□ ̄||)...I will reread this manga after the mysterious girl will appear...