Carrier Recovery, Frequency and Phase offset in (CP)FSK
If the two nodes run the same clock i would know perfectly where the signal starts from the end of the first chirp, after the fixed period of pause. In this case the signal i try to demodulate would have no phase shifting, correct?!


Wrong. The signal travels a distance. The distance it travels inherently means you get a phase shift – a full period ($2\pi$) for every wavelength (that's kind of the definition of wavelength, isn't it).

The signal gets reflected. Reflection often also leads to a phase shift. 

The system with which you produce and measure the physical signal has a phase-shifting behaviour, too.

The only case where you'd not see a time shift is when all these effects add up to a multiple of $2\pi$ (because periodicity).


  If my clocks run differently, i will reconstruct a different signal, right? If yes, why is shifted in phase? 


It's shifted in frequency. Frequency is the derivative of phase. That means that the phase shift is now a linear function of time.


  Can you point me out how to adjust, if possible, this offset or to know where to sample the signal? 


To correct a statically phase-shifted signal, you'll need phase correction. To correct a frequency-shifted shifted signal, you'll need frequency correction.

In analog thinking, you typically employ phase locked loops (PLLs) of first order (static phase correction only) or higher order (frequency shift, or even frequency drift).


  Is this effect something like a Doppler?


The Doppler effect leads to a shift in frequency, too. But it's a different thing.