The general answer is - yes, you must have missed something in your rig as this is not what it should be doing.
I can think of these potential reasons:
1. Magnet Targets are too close to one another (less than 4 pixels) and when you assigned the metadata ID with the Smart Magnet Rig Panel it went to the wrong Magnet Target.
2. You have duplicated an existing MT inside the body symbol which already had metadata ID for the other arm, so Magnet Joint gets confused.
3. You have duplicated the symbol instance of the arm AFTER tagging it and attaching to one of the MTs so both arms snap to that one MT.
Easiest solution would be to select all symbols on stage, break all links using the broken chain button in Smart Magnet Rig Panel and then re-create them properly, i.e. assign the IDs correctly using the chain tool as described in the tutorials.
It is important to understand that metadata is instance based - you assign it via the panel to a symbol instance that has already been placed on the stage. This is why you can have unique IDs for two arms which are instances of the same Library item; one usually flipped horizontally.
It should ideally be done during the preparation stage for animation in a single key and then you can copy/paste your layers/frames into another file and animate. The metadata is retained when you create new keys as long as you don't delete the symbols from the layer. In all versions but Flash CC the standard 'convert to keyframe' works just fine. In Flash CC you must use our 'Convert to Keyframe Advanced'. You can also swap symbols and the metadata will stay.
Please, let me know if this helped you solve your problem.
If not, I'd be happy to look into your rig and fix it, if you would email it to me: firstname.lastname@example.org