The gemara says how do we know that the blood of a korban becomes invalid if it isn't sprinkled on the miz'beiach before "shekiah", and learns out from a pasuk that the blood must be sprinkled the same day that the korban is sacrificed. Rashi explains that we need this special source for a case where the blood was left on top of the miz'beiach to teach that it can become invalid even if לינה occurred at the top of the miz'beiach. Rashi understands that for a typical case where the blood isn't sprinkled the same day, we don't need a special source to invalidate it, since sprinkling can't take place at night and the next day it would certainly be passul like the parts of the animal that are burned on the miz'beiach. Tosafos disagrees with Rashi and says that we need this pasuk to teach that the blood becomes invalid to be sprinkled at sunset, even before צאת הכוכבים which is normally what we consider night. Tosafos explains that even after sunset would still fulfill the requirement of sprinkling by day, we therefore need this pasuk to invalidate any sprinkling after sunset.
In Brachos 26a the Rabbonon consider the time for mincha to be until "erev". Rabbeinu Yona explains that the term "erev" in that context doesn't refer to צאת הכוכבים, rather it refers to sunset. Rabbeinu Yona points to our gemara where the term שקיעת החמה refers to actual sunset with is about 72 minutes prior to צאת הכוכבים. Being that the blood of the evening korban Tamid must be sprinkled before sunset it would follow that in the context of davening mincha, it must be done before sunset. The main activity to validate the korban tamid is the sprinkling of the blood so it would follow that the tefillah of mincha would be dependent on the sprinkling of the blood. Rabbeinu Yona's source for limiting the time of mincha until sunset is completely dependent on learning the definition of שקיעת החמה in our gemara like Tosafos to refer to actual sunset.
The Sha'agas Aryeh (17) has a very long Teshuva where he strongly disagrees with Tosafos and holds that the blood of the korban would only become invalid from being sprinkled at צאת הכוכבים not at sunset. Based on this he writes that the term "erev" in the context of davening mincha is also until צאת הכוכבים, not sunset. He therefore rules that one would be allowed to daven mincha even after shekiha (as chassidim typically do) because even the blood of the Tamid after which mincha was modeled can be sprinkled until צאת הכוכבים. In truth, the Rama (o.c. 233:1) also writes that the time of mincha extends until צאת הכוכבים which can also be read into the term לילה used by the Shulchan Aruch. It is the opinion of the Gr"a (261) that we tend to follow who considers anytime after sunset to be safeik layla, and considers bein hashmashos to last for only 15 minutes or so after sunset at which point it is considered צאת הכוכבים. See the footnotes on Sha'ages Aryeh (footnote 13) where he quotes many opinions who agree with the sha'agas aryeh that mincha can be davened until צאת הכוכבים.