Application enquiries are treated differently from repayment information. The latter has to be reported monthly within 10 days of EOM. However the situation is different for application enquiries. Credit providers can only access credit bureau data in very limited scenarios, the main one relevant here is that they can access credit history when an application is made for credit, what the law requires though is that they reveal as a precondition the circumstances of that credit. So the bureaus know as soon as the provider pulls your file and it instantly becomes part of that record.
However while it becomes part of your record immediately what the bureaus show on your credit file is what is disclosed to others. To use a specific example therefore if you applied for a CC the day after applying for another, yes the first one may well be on your record, indeed multiple applications in a very short time is a major indicator of financial stress and hence one of the first thing credit providers look for (and hence the bureaus definitely want to show as it adds value to their service). Same day applications may work but credit file update is close to immediate i.e. you should be applying within seconds or minutes, not hours.