"Vomit" is not a recent addition to English, and nor does it have a peculiar pronunciation. Yet, the past tense of vomit does not follow the notion that a vowel followed by a consonant and emphasis on the consonant. (For example, past tense of 'emit' is 'emitted'.)
The crucial thing is that the last but one syllable of "vomited" has no stress. Not even secondary stress. So the final consonant doesn't double. By contrast, the last but one syllable of "emitted" has stress (because the last syllable of "emit" has stress).
This issue is raised in this question, to which a good answer is given.
- (No stress) marketed, budgeted, edited
- (Secondary stress) combatted, formatted
- (Primary stress) patted, petted, pitted, potted, rutted