Hi,
When ticking the Use Update Panel checkbox on the default form in the sample site it works for me.
![Image Text](https://content.screencast.com/users/DavidTK/folders/Jing/media/fecafda0-0dee-40ba-ab72-1deb14a53bd8/2019-02-27_1004.png)
Perhaps you have to update your form settings
![Image Text](https://content.screencast.com/users/DavidTK/folders/Jing/media/18aec162-a0a4-4969-9f94-d70f14bb9b04/2019-02-27_1006.png)
to not redirect after submit? If it still doesn't work what adjustments have you made to the cloned Web Part?