I have heard some American English speakers saying the word "tag" like [tεg], but the [ɛ] vowel is somewhat lengthened. Is that a specific regional accent? I can't find this pronunciation on standard dictionaries.
You're right; some American accents raise the vowel /æ/ to [ɛ] and even to [e] before a /g/:
- In New York, New Orleans and some Inland Northern American accents, /æ/ before /g/ is usually realised as [ɛə].
- In Minnesota and Wisconsin, it's [eː~ej].
- In Northern Mountain US and some Canadian accents it's [ɛː~ɛj]
- In some Southern American accents, it's [æ~æɛə]
This phenomenon is called ‘æ-raising’ as explained by Wikipedia (all the above transcriptions also come from that article). This raising also occurs before the nasals /m n ŋ/.
Dictionaries don't show regional differences, they only give phonemic transcriptions.