I hope I don't screw-up adding my lil' diagram..but here goes
lets use terminology that reflects what is goin on... are we not actually aligning with the earth's polar axis? ("pole-stars" whatever, are merely a convenient indicator).... we create the angle of 'tilt' to get our base parallel with a base as it would be if we were on the equator.
this then allows us to pivot the base, around that axis, in 'equal and opposite' rotation to the earth's rotation, thus staying fixed on the same point over time.... as opposed to "pointing to the pole" we are pointing parallel...
think of it like a conrod always pointing at the piston...the gudgeon-pin is parallel to the crank...
as for "declination"..is that to do with the tilt of the earth's axis relative to our orbital-plain??
jargon annoys me
cheers
Russ