Nerevar was like the "One Real Good Guy", he was down right determined to not let the tools get in the wrong hands, the Tribunes wanted the power of the Hearth, they had to kill Nerevar to get it. So thats like the story you put in between the two parts: 1 - When Nerevar took the tools from Dagoth Ur, and, 2 - When Azura punished the tribunes and it's race?
A better timeline:
1) Daggoth Ur discovers that Kagrenac is creating the Numidium.
2) Daggoth Ur tells Nerevar about it.
3) Nerevar consults the Dwemer king, Dumac, about it.
4) Dumac and Nerevar bicker and quarrel angrily over the issue.
5) The argument over the Numidium and the use of the heart leads to the Chimer/Dwemer war.
6) In the closing throws of the war, Kagrenac turns on the heart with his tools, and----
7a) All the dwemer disappear.
7b) The dwemer become part of the Numidium, it activates, and ALMSIVI defeats it, by stealing its godhood, through a mini-dragon break caused by their later apotheosis....
8) The tribunal and nerevar leave the tools in the posession of daggoth Ur, while they consult on what to do with them.
9) The tribunal wish to use the tools to better their people. nerevar objects, and has them swear on oath to Azura that they will not use the tools.
10) Nerevar and the Tribunal return to the heart chamber to find Daggoth Ur driven mad by the tools and the heart.
11a) Daggoth Ur kills Nerevar.
11b) Vivec, Almalexia, and Sotha Sil kill Nerevar after they and Nerevar drive off Daggoth Ur.
12) Vivec, Almalexia, and Sotha Sil use the tools on the heart to become immortal god-kings, and re-write the fabric of reality and history so that they have always been such. (See 7b)
13) Azura becomes FURIOUS with the Tribunal, for violating the oaths that Nerevar made then swear. In retort, The Tribunal mock Azura, and tell her that the Chimer do not need her as a goddess, because the chimer have THEM now.
14) Azura gets SERIOUSLY PISSED, and curses the Chimer race, transforming them into the Dunmer.