I experience this as well, but not in a consistent manner. After pasting, sometimes my cursor will be at the top, sometimes just a few lines up from the end of my paste. If I paste and hit Enter to see where my cursor actually is, sometimes I get a new line at the end of my pasted content, sometimes it's a few lines up, sometimes it's at the very top of the note. This is all when pasting plain text, as I don't dare paste anything with any formatting into Evernote. If I do, I'll have to manually fix the formatting because Undo still doesn't work. This happens on the desktop version (6.06) on Win7 and Win10.
Downloading 6.1 now...
Update: on first use, it appears to have been fixed, but I'll give it a few days. Now I have to go remove the add-ons that it didn't ask me to install every time I update (Outlook, IE).
Update: now it's even weirder (current version 6.1.2.2292). Now when I paste, the cursor is a few lines below where I pasted. If I hit Enter once, nothing at all happens. If I hit Enter twice, a line break gets added several lines below my paste. This happens when pasting from another or the same note in Evernote, as well as from outside Evernote.