I believe that the iOS devices only use the BBcode editor, and because you used the Rich Text editor to create the signature, that would be where the conflict lies. You'd have to completely remove the signature, save it, then re-create the signature if you want to switch between the two.
Editing Signature only showing bbcode in plain text - Page 3
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I was editing a post on my computer today that was originally posted from my iPhone and it was showing code but gave me a link to change it to rich text. I think this pretty much confirms what you told me and it's my iPhone causing the issue with my sig. Thanks for your help.