You should continue to expect the qualities that originally attracted you to the consultant to be present. You should expect to continue doing business with the individual you interviewed and hired not another resource that is brought in without your knowledge and/or consent. It is acceptable, of course, for your advisor to maintain staff and utilize resources of their own choosing, but beware of the consultant who disappears for long periods, leaving someone else to take up the slack.
You should also expect progress reports, ongoing information about the issues and concerns coming up, and to be involved in their resolution. You can't hire a consultant and turn over the reins. You need to work jointly with your consultant to keep yourself involved and up-to-date on project progress.
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