I had the same issue, with the same Westcott product. In fact, it doesn't fit into any light I've ever used or owned, including the Profoto D1, Rovelight 600, Speedlite cold shoe brackets, Broncolor heads. Umbrella shafts are normally round and 7mm or 8mm. The Westcott hexagonal shaft doesn't fit the standard, and more aggravatingly, the specs sheet for these umbrellas just says "7mm tapered tip" and photos on their website (at the time) showed the model I bought as having a round shaft.
I wrote to Westcott pointing this out, and the response I got from their customer support prevented me off buying anything else from them. They wouldn't acknowledge that the shaft was non-standard, they just told me "All of our products with umbrella shafts have always had 8mm shafts". They also did not have a copy of their own product to look at and confirm, they told me their umbrellas have round shafts and asked me to send them photos of it! This gave me the impression that Westcott stuff is drop-shipped from overseas and their CS people don't even know what the current versions of their products look like.
They also couldn't tell me which of their other products had this non-standard hexagon shaft. At the time, I was considering buying some of their umbrella-style softboxes, but I could not do so with confidence that they would fit into any of my (non-Westcott) speedlite brackets. Their solution to my new umbrella not fitting any of my existing lights or brackets: "I shared this with the product manager, but my best solution to you is our # 5015 available through our dealers/retailers for only $29"
EDIT: Edited to replace paraphrased quotes from the fjwestcott CS rep with actual copy-pasted quotes from her email reply.
This is the photo I sent them:
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