This is simple pre-echo. Nothing is wrong with your setup. Most pure analog recordings exhibit this to some degree or another. The magnetic signal on the tape "bleeds" onto the adjoining section when the tape is spooled onto the reel and they overlap - the length can vary depending on reel size (7 or 10") and the tape speed (7 1/2, 15 or 30 ips). This is often referred to as "print through".
-Richard
-Richard