Hi,
Information on Google Scholar can indeed take "up to" 6 months to update. Updates happen when Google Scholar's tools crawl the site, but they do not share a schedule for this. As far as I am aware it is not possible to push the data to Google Scholar either. I have heard that in extreme circumstances it has been possible to request that Google Scholar crawls a site on demand, but this is very rare.
When Google Scholar says it can take up to six months, they are covering themselves a little. It could happen tomorrow (but it would be unlikely), but it probably won't take six months. It just depends on when the site was crawled last time, and when the next crawl is due.
Jonathan