Which groups of Americans pronounce -ing |ŋ| as -inG |ŋg|?
Solution 1:
The only specific type of American English that I have heard described as having [ŋg] in place of [ŋ] is a certain kind of New York accent. See the prior question “ng” in “wrong of me” pronounced [ŋɡ]
The commonly cited example is "Long Island" with [ŋg].
However, Araucaria's answer to the question Why do some people pronounce "singer" as "singGer"? says "many varieties of USA English" may show [ŋɡ] in this kind of context.
Solution 2:
On vowel-nasal-plosive syllable rimes
While I can't tell which groups do what you allege, I can tell you that it is not permitted under the normal phonotactic rules that apply to Modern English.
That's because that if a syllable ends in a nasal and a plosive, that plosive must be either of the two coronal plosives (/t/, /d/) or else it must be the unvoiced plosive whose place of articulation is the same as that of the nasal used. Specifically:
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If it's the coronal nasal /n/, then only the two coronal stops, /t/ and /d/, are allowed, such as in sent and send. You can't use any labial or velar stop with /n/.
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If it's the labial nasal /m/, then besides the coronal stops (such as in dreamt or schemed), /p/ is also allowed because it's the unvoiced labial plosive to go with the labial nasal, /m/, such as in bump.
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If it's the velar nasal /ŋ/, then besides the coronal stops, /k/ is also allowed because it's the unvoiced velar plosive to go with the velar nasal, /ŋ/, such as in bank.
Therefore the only voiced plosive that can end a syllable following a nasal is /d/. You cannot have voiced -VNg or -VNb in Modern English, only unvoiced -VNk or -VNp.
Notes
Words like lamb and dumb and tomb use an orthography that was set way back when we could still say other voiced stops in that position.
In singer there is no plosive, while with finger the voiced plosive is attributed to the start of the next syllable, not to the end of this one.
That’s also what’s happening with the stereotypical "long giland" pronunciation mentioned elsewhere on this page, with the /g/ appearing not at the end of the syllable with the nasal but rather at the next syllable following it.
Related.