Files downloaded and analysis completed!!
Your PDF file doesn't contain any transparency whatsoever. It is a PDF/X-1a 2001 file based on PDF 1.3. Neither PDF 1.3 nor PDF/X-1a support “live transparency” (or for that matter ICC color management or many other modern PDF attributes).
I will assume that your original InDesign document indeed did use live transparency. But when you export to PDF/X-1a (or any version of PDF less than PDF 1.4), all transparency must be flattened into opaque objects. In this case, the simple transparency you used in the InDesign document is emulated via use of Overprint. (Overprint is not considered best practice for modern PDF publishing workflows!) You can readily see what is going on using the Output Preview tool of Acrobat Pro.
Unfortunately, very few PDF readers support display of overprint. Although Adobe Reader and Acrobat support full and proper display of overprint if you have the correct preferences and modes set, neither the iOS nor the Android Adobe Acrobat Mobile products support display of overprint; the overprint attribute is effectively ignored and you end up with the visual anomalies you originally described and that appear in the screen shot you provided. I personally do not know of any mobile PDF readers, including those provided by Apple in iOS or Google in Android that support overprint display.
Workaround? Ditch use of PDF/X-1a which depends on overprint for emulating some transparency effects when PDF is created with flattening. Our recommendation is to export PDF/X-4, a much more modern standard that fully supports live transparency and color management. With any halfway modern RIP or DFE for printing, content that originally contained transparency will render/print better and faster with PDF/X-4 with live transparency maintaining until the RIP process where transparency blending and color management occur than with PDF/X-1a with pre-flattened transparency (which can yield weird stitching and flattening artifacts. The live transparency in such PDF/X-4 files will also display without problems in all Adobe desktop and mobile Acrobat / Reader versions as well as many third party PDF viewers.
Let us know if you have further questions and enjoy the rest of your weekend.
- Dov