The following simple reproduction demonstrates that the second OutputStream passed to hudons.remoting.TeeOutputStream gets data written to it twice (unexpected/bug), wheres the first OutputStream only gets it once (as expected). The issue is so simple, I have no idea how this isn't a known bug causing all sorts of issues, so I assume I'm missing something.  Although maybe it only affects local FilePaths, and maybe this ticket is related (was closed as can't reproduce):

https://issues.jenkins.io/browse/JENKINS-38520

Also of note, I switched the import to 
import org.apache.commons.io.output.TeeOutputStream and it behaves as expected, (each stream/file getting messages once.)
 
 

import hudson.remoting.TeeOutputStream  
//import org.apache.commons.io.output.TeeOutputStream 

File file = new File("test.txt")
File file2 = new File("test2.txt")
OutputStream os = new FileOutputStream(file)
OutputStream os2 = new FileOutputStream(file2)
TeeOutputStream tos = new TeeOutputStream(os, os2)
PrintWriter writer = tos.newPrintWriter()
writer.write("testing ")
writer.flush()
assert file.getText() == "testing "
assert file2.getText() == "testing testing "