Discordance in gene signature behavior between bulk and single-cell RNASeq
One explanation could be that your mapping of clusters to timepoints is not accurate. There are other methods you could look at for doing this, for example scMap, scPred, or Seurat v3 (disclosure: I am one of the Seurat developers).

Another possibility is that there is some problem in the calculation of the activation signature. You could instead look at the expression of the 24 genes themselves in each cluster (for example by drawing a heatmap).

The difference between bulk and single-cell here could also be biological. This could happen if the increase in expression of those genes in bulk was due to a change in cell type frequency over time rather than increased expression.