highfrequency signal on ground
At 2.5 GHz, the wavelength in free space is only about 120 mm or 5 inches.  That means if your distances exceed about 12 mm or a half inch, you don't have a lumped system anymore.

It's not clear what exactly you did, but it seems that you are measuring some signal at -40 dB where you expected none at all.  First, none is never realistic.  Second, this not being a lumped system, exactly how you measured it is significant.

The fact that a 2.5 GHz signal shows up somewhere else nearby attenuated by 40 dB doesn't by itself seem surprising.

You say you measured this "on the ground plane".  This brings up the question of how exactly you measured this, which you haven't stated.  You also seem to be under the false assumption that every place on the ground plane should be at the same voltage all the time.  That's the desire, and is often a useful approximation, but at 2.5 GHz you can't just wave your hand at such things.  The exact geometry matters, as does the route of the return current to this oscillator.