I'm not aware of any guidance from the IRS that says anything about non-dependent adult children on their parents' policy.
For the definition of an eligible individual, Section 223(c)(1)(A) of the tax code says:
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(A) In general The term “eligible individual” means, with respect to any month, any individual if—
(i) such individual is covered under a high deductible health plan as of the 1st day of such month, and
(ii) such individual is not, while covered under a high deductible health plan, covered under any health plan—
(I) which is not a high deductible health plan, and
(II) which provides coverage for any benefit which is covered under the high deductible health plan.
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It says only that you must be covered by the HDHP, nothing about who is the policyholder.
Regarding the contribution limit, Section 223(b)(2)(B) says:
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(B) in the case of an eligible individual who has family coverage under a high deductible health plan as of the first day of such month, $4,500.
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The cost-of-living adjustment has raised the family contribution limit for 2018 to $6,900.
Section 223(b)(5) requires married individuals who are both qualified individuals to share the family limit, but says nothing about others on the policy:
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(5) Special rule for married individuals In the case of individuals who are married to each other, if either spouse has family coverage—
(A) both spouses shall be treated as having only such family coverage (and if such spouses each have family coverage under different plans, as having the family coverage with the lowest annual deductible), and
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Section 223: <a rel="nofollow" target="_blank" href="
https://www.law.cornell.edu/uscode/text/26/223">https://www.law.cornell.edu/uscode/text/26/223</a>
