Did you explicitly define the in the Hyperlink panel? Or only in text?
Set up them correctly in the Hyperlink panel.
Acrobat is reading out Hyperlinks depending on version and settings, but only when you set it up in InDesign’s Hyperlink panel you will get correct results.
Not totally true. You can always add links in Acrobat after the fact.
But the question was here in the InDesign forum and what is wrong with exported URLs and why they behave different.
How are you exporting the PDF: PDF Interactive or PDF Print? If you are exporting Print, you will need to check the box: Include Hyperlinks