Some questions about the specific speed (Ns) of hydro turbines

So we all know the basics behind specific speed Ns of hydro-turbines.

$small{mathsf{Ns = RPM x sqrt{(P)} / H^{1.25}}}$

where P is the power output and H is the head. The theory is that once you know the Ns for that model of turbine, you are able to find out either the RPM, power output or head if you are given absolute values for 2 of the 3 mentioned variables.

Let’s say I have a turbine with a known Ns. If my head increases but my power output remains constant due to say, reduced flow, then the RPM will increase since Ns is fixed. So far, so good.

However, if my head remains constant but my power output increases due to increased flow, then my RPM must decrease since Ns is fixed. But if we think about it that doesn’t make sense…the RPM must be increased for a larger power output, no? Is there something wrong with my understanding of Ns?