I have a feeling it's nothing to do with the splash screen itself that pops up and is just something to do with opening Opera in incognito mode after Opera has been updated automatically by the task in the Windows task scheduler. This might be some scenario that Opera doesn't handle right.
I might try to play with this by installing the previous build and letting it update via the task and then starting Opera in incognito mode and then closing the window to see if the non-private session gets lost.
For now, do a test the next time you notice that Opera has updated when you open it in private mode. Instead of closing the private window with its X, click the menu button at the top left and choose "exit" to close that private window to see if the non-private session remains in tact when you start it back up.