Through Space and Time
Perl 6, 47 46 bytes

-1 byte thanks to nwellnhof



{Set(@^b X&lt;=&gt;Date.today.year)&gt;2,max [Z==] @^a}


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Anonymous code block that takes two lists and returns a tuple of booleans, with the first element being whether you traveled in time, and the second being whether you didn't traveled in space.

Explanation

{                                            }  # Anonymous code block
     @^b X         # Map each element of the year list to:
          &lt;=&gt;      # Whether it is smaller, equal or larger than
             Date.today.year  # The current year
 Set(                       )    # Get the unique values
                             &gt;2  # Is the length larger than 2?
                               ,
                                    [Z  ] @^a   # Reduce by zipping the lists together
                                max       # And return if any of them are
                                      ==  # All equal