With delta reserve amex, additional free cards are issued as delta platinum amex. But spending goes to primary cardholder account. Additional cardholders don't get any of the platinum amex benefits (free checked bag, early boarding).
I think paying $150 for additional delta reserve card grants only lounge access. If you want an additional card with free bag/early boarding benefits for your spouse/family member, it is cheaper to get a separate delta gold amex card in their name.
Of course this only applies if they are traveling separately. If all passengers are on same PNR with primary reserve cardholder then they should get benefits.