Is more fuel consumed immediately when spinning reserve is brought on-line?
In a coal or nuclear plant, the thermal power changes very slowly, perhaps 10-20% per hour. To have power available for spinning reserve, the steam turbines are run at a lower power than the boilers, the main throttle is set so that there is some steam available but not used. The excess steam bypasses the turbine and its energy is wasted. If more power is required, the steam valve can be carefully opened and the power delivered increases. For a big steam turbine this might still take 30 seconds.

So to a first approximation the slow thermal plants consume fuel for the full total of actual power + spinning reserve.

You have a good question about the timescales.
At the shortest timescales, fractions of a second, the frequency is passively stabilised by the inertia of all the generators (and rotating loads).
At longer timescales it's entirely up to the control systems adjusting the power of each generator, and depends on the transient power response of the generator.

Some time back I found a very good presentation by John Undrill, called "Power Plant / System Dynamics and Control" presented at a NREL / EPRI workshop, May 2013.
I can't find a copy of the document to link to now, see if you can find a cached copy somewhere.