What SCORM version are you using? SCORM 2004 has some navigation control maybe that is the difference.
For SCORM v1.2 we call LMSFinish() which is the SCOs last responsibility. I believe that Moodle refers to this method as the “close communication” method in their documentation. Does it work when the course is launched in the same window non-mobile? And one more question, which version of Moodle? Thanks for bringing up this issue, I really like Moodle!