That "make our user experience better" and the use of pop-ups are seemingly in conflict, then.
Modern website user experiences typically don't include pop-ups.
Apple states this:
... Block pop-up ads and windows in Safari - Apple Support
More generally on pop-ups, from some folks known for UI designs:
... https://www.nngroup.com/articles/popups/
Safari on iPad does not allow customization of the pop-up blocking. (Safari on macOS does.)
On iPhone and iPad, your developer will want to employ newer approaches that avoid the pop-ups, or you will want to expect this message. (Some potential options)
You can certainly submit feedback to Apple, such as adding customization to the pop-up blocker:
... Product Feedback - Apple
I would expect better results avoiding the pop-up.