I couldn't find the answer, so can anyone answer for me?

Early Third Era, by Tiber Septim to recover the pieces of the Numidium, so probably not long after the conquest of the Summurset Isles.

Shortly after Reman Cyrodiil was crowned emperor, so around 1E 2703. The Tsaesci submitted to Reman at Pale Pass when he proved he was a Dragonborn, and became his bodyguards and advisors.

Actually, Skyrim's gotten me thinking about the Tsaesci. Since they invaded Tamriel for the sole purpose of finding a Dragonborn, it's possible that Reman's assassination wasn't just because the Potentates were jerks.
I actually think Versidue-Shaie was telling the truth when he said "I have been and will continue to be Potentate Versidue-Shaie, an alien welcomed kindly to your shores. It will be my duty to protect my adopted homeland, and I pledge to work tirelessly at this task until someone more worthy takes the burden from me" (of course, take the 2920 books with a grain of salt, they are works of fiction after all, though the author based them on fact).

However, they're really big on symbolism and myths. So for Reman to be, in their eyes, a true Shezzarine, he needed to be killed, possibly by being stabbed in the heart or having it cut out.

I know Carlovac Townway (author of 2920) says Reman had his throat slit, but it's possible he had his heart cut out afterwards, or perhaps Mr. Townway got that one detail wrong.

Like a certain Tiber Septim after him?

Was he even that bad? I remember it being said that he was /plotting/ to take over but did he arrange the deaths of the Emperor and his heirs? All I remember is that an Imperail Fortress was destroyed in Dawnstar and that in response he tried to abolish local rulers private armies to prevent such a thing happening again, with the Fighter's Guild - then the Syffim of course - established to kind of centralise the local rulers source of soldiers; sounds pretty logical to me, just another way that the Tseasci elevated the Empire whilst they were there.

http://imperial-library.info/content/skyrim-rise-and-fall-blades is a good history of the Blades.

You are an awesome librarian, Lady N.