I don't know Alignmaster, but FWIW the analogous SynScan feature also slews away then asks you to bring the star back, first in Alt, and during the second step, in Az.
However, unless your mount is perfectly level, neither adjustment will perfectly re-centre the star. The SynScan manual is clear about that. You're only to touch one set of controls during either step and bring the star as close as you can to the centre. In fact, during the Az adjustment step, you're supposed to bring the star as close as possible to where it ended up after the Alt adjustment, not the centre.
Regarding time zones, I always use 0 and enter the UTC time.
Cheers
Steffen.
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