[KRHill91]

There's no real classification type for an alumni initiate.
The membership types as described on the website are as follows:

Traditional Membership
Since 1929, ESA International's traditional members have used their vast support network of local chapters to excel in community education, service and philanthropy. Their "hands-on" endeavors provide more than 650,000 direct service hours and over $10 million for charitable causes each year.

Collegiate Membership
ESA collegiate membership is available on participating campuses across the nation. On college campuses that have not yet colonized an ESA chapter, there are opportunities for interested individuals to assist in the colonization process.

Member-at-Large Membership
Share ESA’s benefits and support ESA activities and projects without being a chapter member.

Legacy Membership
This membership is available to close family relatives of existing

Élan Membership
Élan stands for Education–Leadership–Affirmation–Networking. This membership is youth driven, providing middle school and high school age members with opportunities to develop personal leadership skills through service-oriented activities.

DESA Membership
DESA's (Debutante of Epsilon Sigma Alpha) have their ESA membership fee paid in full when they decide to join ESA. They are legacies.