I understand that the Median of Ratios Method is used to normalize gene counts. However, I am concerned that this normalization may be problematic for time series data in which counts may increase over time across samples. Have the developers taken this into account when analyzing time series data, and is there a suggested method for normalizing count data across samples for time series data?

RNA-seq without any internal controls measures relative changes, it cannot be used to assess absolute changes in abundance.

Researchers who are interested in tracking absolute changes will spike in RNA or cDNA e.g. spiking in amounts of mRNA from another organism. If you do this you can provide those control features to controlGenes when you run estimateSizeFactors, and then run DESeq() as normal.