The Sitecore Publishing Service module replaces the PublishManager API and in most cases should work as you expect. SPE implements the use of the PublishManager but in a way that does not appear to trigger the SPS code.
Below is an example on how to queue publishing jobs to appear in the Publishing Service dashboard.
$database = Get-Database -Name "master"
$item = Get-Item -Path "master:" -ID "{110D559F-DEA5-42EA-9C1C-8A5DF7E70EF9}"
$targets = @()
foreach($publishingTarget in [Sitecore.Publishing.PublishManager]::GetPublishingTargets($database)) {
$targets += Get-Database -Name $publishingTarget[[Sitecore.FieldIDs]::PublishingTargetDatabase]
}
$languages = [Sitecore.Data.Managers.LanguageManager]::GetLanguages($database)
# Item publish with children
[Sitecore.Publishing.PublishManager]::PublishItem($item,$targets,$languages,$true,$true,$true)
# All Items
[Sitecore.Publishing.PublishManager]::PublishSmart($database,$targets,$languages)

Publish-Item
uses SPS (at least in my 9.0.1 with SPE 4.7 and 5.0), but if I add the-AsJob
flag, it uses the old publisher. I understand why this happens, but it's not very logical since SPS will always be a job.