No doubt the timing of their statement is one of the things they'll consider, but in principle this phrase refers to how rather than when the news appears in the media.

It says they will have a statement ready for the media, but it will be made public "según cómo trascienda la noticia". In other words, they're not planning to release it straight away. So when, or perhaps whether, they release it will depend on (según implies this) "cómo trascienda".

"Trascender" is commonly used to mean being reported. "Según ha trascendido en los medios" means "according to media reports" or "as reported in the media". So "según cómo trascienda" should refer to how the news, the story, is reported: how, as in what angle the media take, rather than when. What I think they have in mind is that they won't release a press statement straight away but will wait to see how the incident is reported. So if necessary they can release a statement to correct unfavourable or inaccurate reporting. They seem to envisage a reactive rather than proactive media position. But the implication seems to be that they may not release the preliminary statement at all if there's no need. It will depend on how the story is covered.