My guess is any domain that uses the promo price, new reg OR transfer will have to pay the $15 Transfer Fee. I can't tell if they are just a reseller for In2net Network Inc, Tucows, and Network Solutions, or if In2net is a partner/sibling company. In2net Network Inc. is listed on ICANN, DotEasy is not
https://www.icann.org/registrar-reports/accredited-list.html
http://www.doteasy.com/terms/terms-and-conditions.cfm
8. Domain Name Registration
Doteasy offers domain name registration and renewal services in partnership with ICANN accredited registrars In2net Network Inc, Tucows, and Network Solutions. Doteasy processes registration and renewal services through these respective registrars at its discretion.
Promotional offers, including special introductory rates, promotional rates, or any non-regular pricing, are only available to new customers and are only valid for the initial term. All domain names registrations will renew at the regular renewal rate.
Domain names which have opted in to the Automatic Domain Renewal service, and any optional features associated with them, will be automatically renewed for the minimum term available for that domain type at the regular renewal rate 6 days prior to expiry. You will be solely responsible for all renewal costs and for any other costs in doing so. Members may choose to opt in or out of the Automatic Domain Renewal service via Member Zone. If your hosting plan includes a free domain name, Doteasy may automatically renew your domain name for you upon expiry as part of your hosting plan's benefits, regardless of your Automatic Domain Renewal settings.
You acknowledge and agree that you may not transfer the domain name registration to another domain name registrar during the first 60 days of the initial registration, or within 60 days of any successful transfer. Doteasy is authorized to deny any such transfer requests.
You acknowledge and agree that Doteasy may, but is not obligated to, place your domain name in a Domain Lock status to prevent unauthorized or hostile transfers of your domain name.
Domain transfer services are included only for active domain names that are either registered or renewed through Doteasy at the regular rate. Members may transfer expired domain names and domain names that were purchased at a promotional rate to another domain name registrar by paying a Domain Transfer Fee. The Domain Transfer Fee is based on the domain type and is subject to any applicable taxes.
General Domain Transfer Fee (.com, .net, .org, .biz, .info, .mobi, .us, .eu, .me, .club, .link, .work, .xyz) US$15.00
Special Domain Transfer Fee (.uk, .tv, .ca, .co) US$35.00