X-13ARIMA-SEATS offers multiple diagnostics for detecting the presence of seasonality in a given time series. These diagnostics tend to be adequate when used for their intended purpose. This may not necessarily be the case, however, when testing a seasonally adjusted series for residual seasonality. Another concern stems from temporal aggregation. Traditionally, quarterly seasonal adjustments are obtained by aggregating monthly seasonal adjustments, and it is possible that the diagnostics yield conflicting results in this situation. A simulation study is done to examine the performance and power of some of these diagnostics; results are presented.