No, it's not normal. I take it, it is a genuine BMW cover specifically for the E93 (other models use different covers): BMW roundel on the hood, adjustable elastic cord around the lower edge, a short (12") zip down the driver-side rear corner, and very tight fit length-wise.
You'll notice there are two breather flaps, one either side of the roof. I'm guessing they allow any air that enters from the bottom to escape, otherwise the cover could be torn off. I always park with the rear of the car facing the prevailing winds, so as to minimise the chance of rain being driven in through these flaps.
Where I live we get torrential rain, high winds (80mph + ), high temperatures (40+ Celcius) and fairly cold nights (- minus 17 Celsius recently); the car is parked in an open area with no protection other than the cover.
I always wash and THOROUGHLY DRY the car before fitting the cover.
The car is always dry when I remove the cover, and the only reservation I have is that movement in high winds may damage the paint, hence the wash and dry procedure before fitting. So far the is no sign of any damage. Oddly enough, I'm more concerned with damage from the sun or frost, than from rain.
I need to get a big garage ASAP.
So yes, if it's allowing water in, I'd be knocking on the dealer's door. After all, it's not a cheap cover.