In real-world contexts, data can be characterized by a streaming nature, unbalanced distribution, data drift over a long time frame, and strong correlation of samples in short time ranges. Moreover, a clear separation between the traditional training and deployment phases is usually lacking. This data organization and fruition represents a challenging scenario for incremental learning agents, i.e. agents that have the ability to improve their knowledge through past experiences incrementally. In this paper, we investigate the combined impact of temporal similarity and unbalanced data distribution on the classification performance of various algorithms from different research fields, including Continual and Online Learning. Starting from three datasets, we create and release different benchmarks that replicate the investigated setting to analyze the performance of each tested method.