I'm not sure I exactly understand the ruling...
1. You play, say, five Outposts.
2. In your clean-up phase, they make you draw 3 cards instead of five. They still need to cause extra turns so are not discarded yet.
3. At the end of your turn, one of those five Outposts (your choice, but it doesn't matter without Throne Room or something) causes your extra turn. The other four still haven't caused an extra turn and haven't tried yet, and will try next time.
4. You play your outpost turn.
5. At clean-up, the Outpost that caused the extra turn has done everything it needs to and gets discarded. The other four still haven't caused an extra turn so are not done with everything they need to do and stay out.
6. At the end of your turn, all four Outposts try to cause an extra turn but fail. Since they fail, the others have a chance to try (unlike last turn). They are now done with everything and will be discarded next clean-up phase (not the one that just happened, it's too late for that).
7. Next player takes their turn.
8. At their clean-up, it is the first clean-up that has happened since the Outposts finished everything, so even though it's not your turn, it's the next clean-up and your Outposts are discarded.