In fact, there is no contradiction between Midrash Tanchuma and Vayikra Rabba. Both maintain that Chur died on the first day, rather than the second.
Tanchuma siman 19 reads:
וירא העם כי בושש משה
בא שש שעות.
נתכנסו ארבעים אלף שעלו עם ישראל ושני חרטומי מצרים עימהם, ושמותם יונו"ס ויומברו"ס, שהיו עושין לפני פרעה כל אותם כשפים, כמו שכתוב: ויעשו גם הם חרטומי מצרים בלהטיהם (שמות ז יא). ונקהלו כולם על אהרן, שנאמר: ויקהל העם על אהרן ויאמר וגו', שמשה שוב אינו יורד כבר. ואותו היום יום ארבעים היה בשש שעות ביום.
אמרו להם אהרן וחור: עכשיו יורד מן ההר, לא השגיחו.
ויש אומרים:
שעמד שטן והראה להם דמות מיטתו מן ההר, ממה שאמרו: כי זה משה האיש.
מיד עמד חור וגער בהם. עמדו עליו והרגוהו.
כשראה אהרן כך, נתיירא והתחיל מעסיקן בדברים.
והם אומרים לו: קום עשה לנו אלהים.
והכל גלוי לפני מי שאמר והיה העולם מה הם מבקשים.
אמר להם אהרן: פרקו נזמי הזהב אשר באזני נשיכם.
אמר אהרן להם דבר קשה, שהנשים מתעכבות בו, שהם ראו כל הנסים והגבורות שעשה הקדוש ברוך הוא במצרים ובים ובסיני.
That is (using ellipses liberally for the first paragraph):
(Pasuk 1) וירא העם כי בושש משה -- 'And the nation saw that Moshe was delayed' -- He came at the sixth hour... (still pasuk 1) וירא העם כי בושש משה -- and the nation gathered unto Aharon and said to him... Aharon and Chur said to them, now Moshe will descend from the mountain, and they didn't listen.
And some say: that the Satan arose and showed them the image of his [Moshe's] bier from the mountain, from that which they said (still pasuk 1) כִּי זֶה משֶׁה הָאִישׁ. Immediately Chur arose and rebuked them. They arose against him and killed him. When Aharon saw this, he feared and began making them busy with busy work. And they said to to him (still pasuk 1) עֲשֵׂה לָנוּ אֱלֹהִים. And all was revealed before He who spoke and the world came into being what they were asking. Aharon said to them (pasuk 2): פָּרְקוּ נִזְמֵי הַזָּהָב אֲשֶׁר בְּאָזְנֵי נְשֵׁיכֶם. Aharon told them to perform something difficult, for the women would prevent them, for they saw all the miracles and mighty acts which Hashem had performed in Egypt, at the Sea, and at Sinai...
Thus, the killing of Chur is explicitly on that first day according to Midrash Tanchuma.
It is true that, on the next day, in Siman 20, Midrash Tanchuma makes reference to the fact that Chur was killed:
ולא עגל בלבד עשו, אלא גלוי עריות ושפיכות דמים, שנאמר: וישב העם לאכול ושתו ויקומו לצחק.
ואין צחוק אלא גלוי עריות, שנאמר: בא אלי העבד העברי וגו' (ברא' לט יז).
שפיכות דמים, דכתיב: יקומו הנערים וישחקו (ש"ב ב יד), ואין לך גדול מן חור שנהרג.
And not only did they fashion the Golden Calf, but also engaged in licentiousness and bloodshed, for it is stated וישב העם לאכול ושתו ויקומו לצחק. And צחוק only means licentiousness as is stated... [pasuk citation] Bloodshed as is stated... [pasuk citation] And you have no greater bloodshed than that of Chur who was killed.
You are right, in your question, that this ambiguous statement of Rashi, and even the ambiguous statement in Tanchuma 20, seems at first glance to be stating that Chur was killed right now, on the second day. After all, it is offered in explanation of צחוק, which happened on the second day.
However, this midrash in Tanchuma 20 is not the primary place that the Midrash Tanchuma states that Chur was killed. That primary place was Tanchuma 19. The wording that Tanchuma 20 uses, ואין לך גדול מן חור שנהרג, implies a fait accompli. Not because it uses the past tense, or passive, because much of the other details are also written in past tense. Rather, because it refers to it as something already known. It is not coming to state that "Chur was killed". Rather, as a way of demonstrating the bloodshed part of צחוק, it notes that Chur's death, which the audience already knows, easily (אין לך גדול) fulfills that part of the definition.
Perhaps one could resolve this messiness and say that there was licentiousness in general and bloodshed in general, as proved by the pasuk citations about the meaning of צחוק. And as an added bonus, the author of Tancuhma threw in this bloodshed of Chur, which happened the previous day. Or perhaps one could say that the Midrash meant to apply צחוק to the entire incident, and thus extends it to the events of the previous day.
Regardless, the author of Midrash Tanchuma assumes people will be reading in context, and so will not be misled into thinking that he was stating that Chur was killed on the second day. And Rashi, who knows the context as well, and is channeling Tanchuma, also did not intend to convey any contradiction.