Every time this happened to me, it was because I dragged a window or tab over there. I would at some point close Safari. Then when I opened it again, it would open on 2nd monitor.
What I did:
When Safari opens on the 'wrong' monitor, grab an open tab, and drag it to the other monitor, then let go. You should have Safari open on both monitors. You should also have a Safari Menu bar on both monitors. Go to the window on the monitor you do not want Safari to open with. Go Menu, File, Close Window (command +W). You should now have only one Safari window open on the monitor of your choice. Go Menu, Safari, Quit Safari. Then try reopening Safari. It should open on the screen of your choice.
I can't find a setting for default screen for Safari.
If it happens again, Make sure the last window you close is on the monitor of your choice.
Hope this helps! Let us know...