The plugin you mentioned is for giving you access to the WP RESTful API.
Current versions of Bitcoin and Altcoin Wallets implement the JSON-API with custom code, not via the WP REST API.
You should follow the instructions given in the manual, under “APIs, APIs everywhere!” -> “Wallets JSON API” -> “Programmatic access to the Transactions API”. You can get the manual in PDF form if you get the bundle download of the plugin from this website. The trick is to pass the user-specific key via the
__wallets_api_key GET parameter, or via a bearer authorization HTTP header. Examples using
curl are given in the documentation.
P.S. As a sidenote, I am currently developing Bitcoin and Altcoin Wallets 6.0.0, which is a complete rewrite of all the code of the plugin and its extensions and adapters. This is an effort that will take several months and will upgrade many aspects of the software suite. One such improvement is that the WP REST API will be used instead of the current JSON-API. When this is out, I will make every effort to provide backwards compatibility via a JSON-API that will be marked as deprecated and will be compatible with version 3 of the current API. Therefore you will not face any unpleasant surprises regarding the app you are building. In any case, I will blog about wallets 6 at a later date, which may be several months into the future. Watch for the release notes of wallets 6, when they become available, before upgrading to this major version of the plugin, because if there is any migration instructions I will make sure to discuss them on the blog. There will be announcements on Facebook, Twitter, the blog, and the RSS feed.