Powershell: Copy-Item from within Start-Job seems to work, but file is missing afterwards

I created the following script block, which should look for a file matching a regex on a UNC path and copy it to the target folder:

$ScriptBlock = {
    param (
        [string]$serverName,
        [string]$ip,
        [string]$fullPathRegEx,
        [string]$target
    )

    if (!(Test-Connection $ip -Count 1 -Quiet)) {
        $msg = "{0} is not responding!" -f $serverName
        Write-Host $msg -ForegroundColor red
        return
    }

    $file = Get-ChildItem -Path $fullPathRegEx

    if ($file) {
        $msg = "Copy-Item {0} {1}" -f $file, $target
        Write-Host $msg -ForegroundColor yellow
        Copy-Item $file $target

#       $cmd = "Robocopy {0} {1} {2} /NJH /NJS /NDL" -f $file.Directory, $target, $file.Name
#       Write-Host $cmd -ForegroundColor green
#       Invoke-Expression -Command $cmd
        $?
    }
    else {
        $msg = "No file matching {0} found in {1}" -f $fullPathRegEx, $serverName
        Write-Host $msg -ForegroundColor red
    }
}

It works fine when called like this:

Invoke-Command -ScriptBlock $ScriptBlock -ArgumentList $server,$ip[$server],$regEx,$targetPath

But when I call it via Start-Job, it doesn't copy the file:

foreach($serverName in $servers.keys)
{
    $regEx = '\\{0}\c$\Data\DB-Backup\{1}{2}*.txt' -f $servers[$serverName], $serverName, $date
    Start-Job $ScriptBlock -ArgumentList $serverName,$servers[$serverName],$regEx,$targetPath -name $serverName
}

The output is there, it causes network traffic, but the target folder remains empty. I'm not quite sure if this happened before as well, but I also get an error for the second server (only tried with 2 so far), saying that the target folder is in use??

I tried it with robocopy as well, which are the commented lines. I would even prefer robocopy, since that provides progress status (still need to figure out how to parse and pass it to the caller). But there I get a similar situation: it works if the scriptblock is called directly, but when called via start-job, it gives me this:

ERROR 123 (0x0000007B) Accessing Destination Directory C:\Users\abv\Documents\DBDumps_20180924\
The filename, directory name, or volume label syntax is incorrect.