Yes, there will definitely be some kind of limit. There is no other way in such shared environments. The only question is whether these limits are communicated transparently or not. Probably not in this case. But given the prices, it's quite understandable.
It's a pretty tough nut to crack. I ran some tests and the IOPS is good on netcup (even better than on the provider where I do not have the same issues), but for some reason I am encountering the exact situation OP is describing. Unfortunately it is not worth it for me to investigate further, so I will leave it at that.