You know you have cracked it because using the proposed system you are able to translate the uncracked language. Also helpful if your proposed system for Linear A makes sense relative to related languages that are not Linear A. Tom's proposed phonetic values work for more than one language.
Not questioning the particular finding, just wondering in general. E.g when linear B or hieroglyphs were cracked, you could check angainst other untranslated texts and see if the translation still made sense.