Checbox fields in data actions need the data in a specific format to update.

[!CBV!] between each value is the delimeter required e.g. Choice1[!CBV!]Choice2 etc.

Note it will try to match on a Choices value first then the displayname if that fails.

When using in REST XML you can use something similar to #string-join(node path e.g. //item/value,'[!CBV!]').