When I asked my original question, I thought that there WAS a contradiction about the direction of the electric fields and so I wondered if there was no such thing as a uniformly increasing magnetic field. Now I see that there is no contradiction about the field direction. But I still have issues with the term "uniformly increasing uniform field".
Suppose we are located in a uniform electric field. That means that the experiments we perform to investigate that field should come out the same when we repeat them, translated a little to the left or right.
But in a "uniformly increasing uniform magnetic field", that is not the case? There is always a "center" to such a field? And by performing repeated experiments with test charges, you can find the center of that field. So uniform in this setting does not mean what I thought it did...