The government
was tracking key health metrics and sharing them at the point Dom was talking about using his iPhone. For instance on the same date, the government did it's first daily briefing and shared infection and death metrics with the public (see
https://www.bbc.co.uk/news/uk-51901818).
Tracking key health metrics and sharing those metrics with the public doesn't mean that there is modelling about the extent to which infections would spread - although we also know that the imperial modelling was released a day later, so while he may have been using his iPhone to make predictions there were also academic teams modelling this that were collaborating with the government at the time (see https://www.imperial.ac.uk/news/196234/covid-19-imperial-res...).
It's also not clear what a 'data system' is in this context - there was clearly an effort to very quickly put something in place to capture data (because it couldn't wait a few weeks/months), but a more robust analytics system will inevitably take more than a few weeks to put in place if not already in place pre-pandemic (a lot of this is about how NHS trusts are structured in the UK, which operate fairly independently). It's not clear to me how quickly is realistic to implement what Dom thought was suitable in terms of a 'data system', particularly as I'm not particularly clear on his requirements (he seems to want an element of forecasting built into this system for instance?), so without knowing what the requirements are can we be confident that what he wanted to build was possible to build, test and implement in his expected timeline?
So I don't think there is a clear contradiction here (and in fact, I think the evidence points to the fact that the statement in the article is probably correct).