Hello Jereon
Unfortunately I never got this solved. I had tech guys from ogone ( who were working with tech guys from prestashop) and between them they didnt get it sorted so in the end I decided to accept defeat and use the sagepay and the prestochangeo sagepay module which is absolutely superb. Also this embeds into your checkout so the customers doesnt even feel like they have left your site.
I tried for weeks to get the ogone module working but my advice for you would be just to steer clear of it.
Sorry
Anthony