Clients expect a report fast, if not at the end of the day, at least within a day or so. So how do you satisfy the Client as well as take time to review the home inspection report and submit a correct and professional one.
The key is to submit an interim report. That does not mean a written one, it can just be a verbal communication to the Client which gives them a summary of your observations. If you find that the house has a several issues, you could pass on the information that there is a lot of work to be done before it can be called liveable. Or if it is about a leaky roof, you could inform that this is something that could take a few weeks to get corrected.
Remember that the Client does not want a point by point explanation immediately but would certainly like to know where they stand. If you could satisfy this necessity and if you could also explain your requirement of reviewing the home inspection report and getting it checked by your supervisor, very few will murmur.