It could very well be set up quickly and to the manufacturer's specs which don't work for your type of playing, or was done in a rush to begin with. This happens often, and adjustment (assuming you have a set of hex keys) is pretty easy.
The clue I'm going with is:
...This happens most on the two middle strings...
This really isn't that big of a deal. If you're not encountering this on the outer strings then your neck is set well, and relief is good. However, your inner two strings probably sit considerably (enough) closer to the fretboard causing the buzz. The easy fix for this is an adjustment at the bridge to raise (you don't need much) the height of the string to match more of the fretboard radius. Check out this video for adjustment.
If above doesn't solve the problem then I'm afraid you may just not be pressing hard enough (I can't judge your experience with bass right now). I only get the feeling of this by the following statement:
...and I can only avoid the buzz by pressing the strings really hard...
To get a clear, loud note out of a fretted one, you may need to press a bit harder than you think (especially if you're starting out, and not used to the amount of pressure required by a bass).
If this is the case, you may want to look more into proper positioning of your thumb on the back of the neck to provide the right anchor point and applied pressure you're looking for.
EDIT: Considering it's a Harley Benton, the setup process was probably just not done properly, and a quick neck/bridge setup may all be all that's necessary. Make sure this bass also has a straight neck (Excuse Guitar World's ads).