How to ensure that FindClusters and ClusterClassify have the same cluster name?

I am trying to ensure that both the FindCluster and ClusterClassify function provide the same cluster name.

To explain this better, I have a minimum working example in which dummy data is organized into 4 clusters.

SeedRandom[1234];
dummydata =
RandomSample[
Table[x^2 + RandomReal[{-0.01, 0.01}], {x, -1, 1, 0.002}]];
ListPlot[dummydata, PlotLabel -> "dummy data",
PlotStyle -> {Black, PointSize -> 0.02}]


fig 1: dummy data

cdummy = FindClusters[dummydata, 4];
ListLinePlot[{cdummy[[1]], cdummy[[2]], cdummy[[3]], cdummy[[4]]},
PlotStyle -> {PointSize -> 0.02}, PlotLegends -> Automatic,
PlotLabel -> "dummy data in 4 clusters"]


Notice the plot legend labeling for the 4 clusters.

fig 2: dummy data organized into 4 clusters

Classifying the dummy data into 4 clusters so that given any data point, I know what cluster it belongs to.

cdummyClassify = ClusterClassify[dummydata, 4]
{cdummyClassify[0.92], cdummyClassify[0.99], cdummyClassify[0.52],
cdummyClassify[0.55], cdummyClassify[0.02]}


Now, I create a cluster classification object which would allow me to identify the data cluster any given point in the future belongs to.

cdummyClassify = ClusterClassify[dummydata, 4]
{cdummyClassify[0.92], cdummyClassify[0.99], cdummyClassify[0.52],
cdummyClassify[0.55], cdummyClassify[0.02]}


Although the classification of data points is correct, the cluster label is not the same as that of fig 2. How do I ensure that the same clustering label is used for both FindClusters and ClusterClassify?

(*{2, 2, 4, 4, 1}*)