The article referenced is suggesting that the rare but serious clotting issues related to the adenovirus vaccines is caused by an errant processing of the spike gene which results in production of truncated spike protein that has soluble properties which results in it being excreted into the body. This soluble spike protein can then cause blood clotting issues when binding to endothelial cells in blood vessels.
So to attempt to answer your question: we expect the vaccine to result in the production of the spike protein in the body which your body then builds an immune response to which protects you from future infection. However, either due to a problem with the vaccine or how the spike protein is created in the body (I'm am not sure which - someone let me know), in rare instances a truncated spike protein can be produced that is slightly different than expected and results in blood clotting issues.