I needed to add event in the code. It's more or less the same. But took me some time to figure out.
rule.addTarget(new
cdk.aws_events_targets.CodeBuildProject(codeBuildProject, {
event: cdk.aws_events.RuleTargetInput.fromObject({
environmentVariablesOverride: [
{
name: 'TAG',
value: tag,
type: 'PLAINTEXT',
},
],
}),
}));