The gemara learns from the fact that the Torah writes by the korban shlomim that it must be slaughtered פתח אוהל מועד that the shechita must take place when the doors are open, not when the doors are shut. The gemara continues to explain that any area where shechita was done had to have some exposure to the inside of the ohel mo'ed, or the u'lam which rashi explains was also called "ohel mo'ed", or to the kodesh ha'kadashim (beis ha'kapores - to allow shechita behind the beis hamikdash in the west). Although the gemara only discusses this requirement regarding the korban shlomim, Tosafos in Yoma 29a writes that the same halacha applies to all korbanos that the area of shechita must be exposed in some way to the inside of the ohel mo'ed.
This halacha of the doors of the ohel mo'ed being open seems to apply only at the time of the shechita not during other avoda, even though the shechita was less avoda-like being that it didn't require a kohein. The Meshech Chochma explains that since shechita was the start of the avoda it had to be in an area where Hashem's presence was visible to connect the avoda to the source of kedusha. Once the avoda begins on the right foot, the remainder of the avoda even it if is more essential follows along - כל העושה על דעת ראשונה עושה ,זבחים בע"ב. It is for this reason that the avoda must begin by day, not by night because daytime is considered when Hashems presence is noticed and revealed. The completion of the avoda such as the burning of the korban could be completed even at night.