But anyone knows the reasons for these changes in signal strengh? A technical explain would come in handy
Here is a hypothesis for newer generation birds, but I will admit it is just speculation:
The beam-shaping in general is done using mechanical reflector design (narrow vs wide beamwidth).
I don't think the satellites employ variable-geometry reflectors, only steerable ones (ie "reverse AzEl mount").
The increase in perceived strength is either due to temporary increase in power output (more spillover and increased side-lobes), or from slight misalignment of reflector.
The power output could be for testing, calibration or whatever technical reason, but are unlikely to be for commercial reasons.
Misalignment could be due to general sat-drifting-out-of-alignment (sats are pulled this way and that by earth, moon, sun etc), or from having to maneouver (during the maneouvering, the satellite may be nudged slightly out of alignment as the thrusters probably aren't arbitrarily directional).
So - any increase in reception strength is most likely due to engineering reasons, and then mostly for alignment.
But this is just me as an amateur satellite enthusiast.
Perhaps someone who knows more can qualify this?