Molecular phylogenies are used as a basis for making inferences about macroevolutionary history. However, a robust phylogeny does not contain the information that is necessary to make many of these inferences. Complex methodologies that incorporate important assumptions about the nature of evolutionary history are therefore required. Here, we explore the implications of these assumptions for making inferences about the macroevolutionary history of Ipomoea – a large pantropical genus of flowering plants that contains the sweet potato (Ipomoea batatas), a crop of global economic importance. We focus on assumptions that underlie inferences of divergence times, and diversification parameters (speciation rates, extinction rates, and net diversification rates). These are among the most fundamental variables in macroevolutionary research. We use a series of novel approaches to explore the implications of these assumptions for inferring the age of Ipomoea, the ages of major clades within Ipomoea, whether there are significant differences in diversification parameters among clades within Ipomoea, and whether the storage root of I. batatas evolved in pre-human times. We show that inferring an age estimate for Ipomoea and major clades within Ipomoea is highly problematic. Inferred divergence times are sensitive to uncertain fossil calibrations and differing assumptions about among-branch-substitution-rate-variation. Despite this uncertainty, we are able to make robust inferences about patterns of variation in diversification parameters within Ipomoea, and that the storage root of I. batatas evolved in pre-human times. Taken together, this study presents novel and generalizable insights into the implications of methodological assumptions for making inferences about macroevolutionary history. Further, by presenting novel findings relating to the temporal dynamics of evolution in Ipomoea, as well as more specifically to I. batatas, this study makes a valuable contribution to our understanding of tropical plant evolution, and the evolutionary context in which economically important crops evolve.