The rule for spelling there is thus:

• A silent `e' on the end of a word indicates that the previous vowel will be long (`tin' vs. `tine')
• When adding a suffix to a noun, double the last consonant unless there's a silent `e', in which case, drop the `e' and don't double the consonant.
• This all means that if you have a noun with a suffix, a doubled final consonant before the suffix indicates a short vowel and a single consonant indicates a long vowel

Of course, that all assumes that you recognize ``tinny'' as meaning ``like tin'' and not solely a word unto itself. Even more obscurely, it requires that you recognize ``tiny'' as meaning (at some point in the past) ``like a tine''. It also only applies to words with simple vowel-consonant endings. But such is English.