I’ve noticed that whenever I’m typing quotes the marker jumps past the second quotation mark if I’m not quick enough. That is to say, I usually start by typing two quotation marks like so “” and then insert the text so I don’t forget the second mark. But more often than not the cursor jumps past the second quotation mark as I’m writing inside the marks making my text look like this: "I"am writing, when I want it to look like this “I am writing”.
I just gave this a crack, and it seems that if you wait for the one second for the quotes to become smart quotes, then it should let you tap left arrow and type in your quote as desired. If you don’t, then when it gets a second to think ¡or! when you hit the space bar, then it moves the cursor to outside the end quote mark when it replaces it with a smart quote, as you describe.
Maybe I’m making assumptions about your setup. Do you have smart quotes enabled? Are you tapping left to go back between them?