Ultimately, this will all come down to a judges interperitation of the law, should it ever get taken that far.
Generally speaking, there is some law that might be used as a guidance. For instance, in contract law, if an agreement doesn't stipulate a time period, then "reasonable time" comes into play, which is where each situation is taken on its merits. Given that a digital railcard requires an internet signal in order to produce one, it's very unlikely that a judge would agree with the interpretation that it must be produced 'immediately'. "on request" is also defined in other parts of law as being 'within a reasonable period of time', so for instance, on request is interpreted as requiring action as soon as is reasonably practicable, not necessarily immediately.
There is no specific case law relating to this point, but general case law does suggest that a standard of reasonableness should be applied. I think any judge would be likely to deem five minutes as entirely reasonable, especially given the problems with mobile telecommunications on a moving train. Having said that, I'd bet good money that the case would never reach the courts, because there would be the potential issue of precedent being set in a manner that would be most unfavourable to the railway.
In strict liability cases, such as in the requirement to produce a railcard on demand, there is a concept of "reasonable excuse" in case law. Someone who is trying to produce a digital railcard and can't because of a lack of signal / lack of available wifi would likely have a reasonable excuse, because there's nothing in the digital railcard literature that requires you to do anything other than load the railcard up on demand.
If the digital railcards had to be produced 'immediately', then they would be available offline through one of the wallet apps.