The Ordinariates' official office book is currently in preparation, but there does exist the Customary of Our Lady of Walsingham of the UK Ordinariate [the Personal Ordinariate of Our Lady of Walsingham].
That contains the Order for Evening Prayer which is very similar to the Evensong of the Book of Common Prayer of the Church of England. It contains the rubric
The Anthem to the Blessed Virgin Mary follows the final office of the day (see pages 151 and 928).
The latter page shows the plainsong settings of the Latin texts; the former lays out a usual translation, the versicles/responses and the collects. There is no indication of posture at all.
The Customary also includes an Order for Compline which is very similar in structure to the Bloomfield office linked in the question (albeit in English, of course), including the responsories* and the prayer Vísita, quǽsumus Dómine, habitatiónem istam. There is no indication of posture.
It's also the case that there is no indication of posture in the [modern] Divine Office for Compline (or, indeed, at all). In the Bloomfield version, indications of posture appear to be lacking — the Order implies standing up to Deus in adjutorium, but omits the customary sitting for the psalms, and anything after that. I can't see where the OP assertion comes from.
In short, there is no indication of posture in any of the Office books. I've never experienced kneeling for the final anthem (either in the Church of England or since joining the Catholic Church in the Ordinariate), and in my opinion the words don't really lend themselves to that.
* The Customary Order for Compline also includes Keep me as the apple of an eye / Hide me under the shadow of thy wings which is not included in the Bloomfield version.