CAP Exempt in other words Exemption from The Quota is meant for those who already have H1B Visa.
Once H1B is filed and approved, the person will be CAP Exempted for the span of 6 years from the date of H1B Approval Notice Validity.
There would be certain exemptions if Green Card Labor is filed and if GC I-140 approved. If GC is not filed, Exemption from The Quota will lapse and person will come under fresh H1B Quota.
If you have the H1B approval Notice copy, please share it with the H1B attorney and they will confirm clearly.