Thank you for your post.
The .ics file will not open in the Calendar app under iOS; only under Mac OS X. If you look at the comments below the Export Records script step, it says "Toggle the "Automatically Open File" option if you don't want the file to automatically open in iCal etc.". That is, if you double-click a .ics file in Mac OS X, it will automatically launch Calendar (previously named iCal). Under iOS, you are limited to the FileMaker work area, and the Share options do not include the Calendar app.