According to this post (asking the same question for the very similar Home Return Permit), the answer is if the Permit expires on 6/20, you will be able to enter China on a flight arriving 6/19, but you may have to leave China by 6/20. However, you can likely extend the permit once you're in China at a police station.
https://www.discuss.com.hk/viewthread.php?tid=30991944

Still, this may be too niche of a question for Flyertalk. I think there's probably only a handful of people on FT who are eligible for a Taiwanese Compatriot Permit. You might have better luck getting a definitive answer by asking a travel forum on a .tw site, or asking on social media, or calling CTS in Hong Kong.