The custom is to wait until actual nightfall to daven ma'ariv on Shavuos, either to fulfill having 50 complete temimos days of sefira (Magen Avraham O.C. 494), or, as the Netziv suggests, because Shavuos is described in the Torah as being celebrated on "etzem hayom hazeh" (VaYikra 23:14), the exact day without adding additional time of tosefes. It seems strange that the Torah precludes our accepting Yom Tov early rather than encouraging or at least allowing us to enjoy and welcome even more time dedicated to kedushas hachag. I think the reason (derech derush) can be gleaned from the Torah's description of the culmination of sefirah.
“Ad m’macharas hashabbos hashevi’is tisperu chamishim yom…” – Until after the seventh week, count for yourself fifty days (23:16). The meaning of the pasuk is to count fifty days until seven complete weeks have been counted, but translated literally the pasuk implies that we have until a full seven weeks have passed to count fifty days, i.e. 50 days can counted any time during this seven week period ends, even on the very last day!
The Rebbe of Tchotekov explains that on each day of the fifty days of sefirah we take another small step in the process of perfecting our character traits, making a stronger commitment to avodas Hashem, and growing in our anticipation for kabbalas haTorah on Shavuos. But what if a few days or even minutes before Shavuos a person suddenly realizes that he has not utilized this time period appropriately? What if, rather than feeling the joy of Yom Tov approaching, a person looks back with regret at the weeks of wasted moments and wasted opportunities that have passed?
The pasuk answers, “Until seven weeks have passed” – until the very last second before Yom Tov arrives – “count for yourself fifty days” – one can still accomplish all of the necessary growth that should have been accomplished in the count of the past 50 days. There is no need to surrender to regret and remorse as so much can be accomplished in even seconds before Yom Tov.
The reason why there is no tosefes allowed for Shavuos is because the Torah wants to maximize the opportunity that we have to prepare ourselves to enter Yom Tov properly. Without proper preparation Yom Tov and kabblas haTorah cannot be celebrated in a meaningful fashion.