You are starting the processes in order, but by default Start-Process does not wait until the command completes before it starts the next one. Since the commands take different amounts of time to complete based on the .PDF file size they print in whatever order they finish in. Try adding the -wait switch to your Start-Process, which will force it to wait until the command completes before starting the next one.
EDIT: Found an article elsewhere on Stack which addresses this. Maybe it will help. https://superuser.com/questions/1277881/batch-printing-pdfs
Additionally, there are a number of PDF solutions out there which are not Adobe, and some of them are much better for automation than the standard Reader. Adobe has licensed .DLL files you can use, and the professional version of Acrobat has hooks into the back end .DLLs as well.
If you must use Acrobat Reader DC (closed system or some such) then I would try opening the file to print and getting a pointer to the process, then waiting some length of time, and forcing the process closed. This will work well if your PDF sizes are known and you can estimate how long it takes to finish printing so you're not killing the process before it finishes. Something like this:
ForEach ($PDF in (gci "*.pdf"))
{
$proc = Start-Process $PDF.FullName -PassThru
Start-Sleep -Seconds $NumberOfSeconds
$proc | Stop-Process
}
EDIT #2: One possible (but untested) optimization is that you might be able use the ProcessorTime counters $proc.PrivilegedProcessorTime and $proc.UserProcessorTime to see when the process goes idle. Of course, this assumes that the program goes completely idle after printing. I would try something like this:
$LastPrivTime = 0
$LastUserTime = 0
ForEach ($PDF in (gci "*.pdf"))
{
$proc = Start-Process $PDF.FullName -PassThru
Do
{
Start-Sleep -Seconds 1
$PrivTimeElapsed = $proc.PrivilegedProcessorTime - $LastPrivTime
$UserTimeElapsed = $proc.UserProcessorTime - $LastUserTime
$LastPrivTime = $proc.PrivilegedProcessorTime
$LastUserTime = $proc.UserProcessorTime
}
Until ($PrivTimeElapsed -eq 0 -and $UserTimeElapsed -eq 0)
$proc | Stop-Process
}
If the program still ends too soon, you might need to increase the # of seconds to sleep inside the inner Do loop.