"Unlocked" isn't a concept that applies to CDMA carriers like Sprint (Ting's underlying network provider), it's a GSM/SIM card thing. There are multiple versions of major phones like the S3 and Note 2, each designed to work on a specific set of networks. If you're looking at an unlocked phone, chances are it's designed for a GSM carrier and doesn't physically have the radio hardware to work on a CDMA network. You need a version designed for use on Sprint.
In addition, BYOD currently has restrictions on what is allowed by Sprint, and one of those is no LTE devices. The S3 and Note 2 are LTE devices, and so are not currently eligible for BYOD.
Bottom line, if you want to use one of those phones on Ting now, it must be purchased directly from Ting. They hope this restriction will be lifted at some point later this year, but Sprint has not formally announced it yet.