Another way of looking at it is to regard the pi network at matching or transforming the antenna impedance upwards in value, to correspond to the tube's optimum plate load impedance.
Typically tubes have a load impedance of a few thousand ohms. Say the antenna is 50 ohms. The pi network transforms this up so that the tube 'sees' a load more like a few thousand ohms instead of 50 ohms.
You can estimate the tube load impedance by (plate voltage divided by plate current). So for a 2500 plate voltage amp drawing 1 amp plate current, load impedance would be something of the order of 2500 ohms (actually a percentage of about 50-70% of that but the principle is the same).
To answer your question, if you turn up the power, for a fixed plate voltage, plate current rises and therefore tube load impedance falls in value. If you turn up the voltage, load impedance rises if the plate current is maintained constant. So the pi network is faced with the job of matching different tube load impedances, which it usually does by changing the tune and load controls.
When operating CW the plate load impedance is a constant value, as the plate voltage and current are fixed. In SSB the plate load impedance changes according to voice patterns so tuning for maximum output on a single tone may produce less efficiency at some other patterns.