If the PDF is a fillable form, you should be able to tap in the fields and start filling in the form. If this does not work for you, can you please share your document so I can understand the problem further?
I recieved your test files. Thank you very much for sharing them. It looks like the file you shared is not actually a PDF Form, but it's a flat PDF file. You'd have to use a product like Acrobat Professional to add fillable fields to the form. There is a feature that we're considering for a future release that might help you fill even flat forms. Please watch for updates!
Thank you again for sharing the files.