My Win10 Pro 32-bit machine started out life as a Windows 7 Ultimate machine with 3 accounts. When I upgraded those 3 now-local accounts were carried along and are all that are on it, so it wouldn't appear that a Microsoft Account is required.
This message occurs frequently (for some value of frequently), see: https://duckduckgo.com/?q=windows+10+you+have+been+signed+on+with+a+temporary+profile&t=hq&atb=v33-7__&ia=web
I had to fix this a while back for a client but used one of the methods discussed in those search results to do so. I should note, though, that this message was coming up on an already established Microsoft Account-linked Windows 10 user account in that case, not a local Windows 10 User Account.
Brian AKA Bri the Tech Guy (my website address is in my profile) Windows 10 Home, 64-bit, Version 1709, Build 16299
Here is a test to find out whether your mission in life is complete. If you’re alive, it isn’t.
~ Lauren Bacall