You can set a redistribute action by powershell
$PackageID = "xxx00004"
$DPGroup = "Name of your Distribution group"
$DPQuery = Get-WmiObject -Namespace "Root\sms\site_xxx" -Class SMS_DistributionPointGroup -Filter "Name='$DPGroup'"
$DPQuery.RedistributePackage($PackageID)
In my environment It did not trigger directly the redistribution.
I needed to redistribute another package and it did the client update package at the same time.
Maybe this can help