Through Space and Time

Perl 6, 47 46 bytes

-1 byte thanks to nwellnhof

{Set(@^b X<=>Date.today.year)>2,max [Z==] @^a}

Try it online!

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:
          <=>      # Whether it is smaller, equal or larger than
             Date.today.year  # The current year
 Set(                       )    # Get the unique values
                             >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

Python 2, 111 109 bytes

lambda S,T:(min(map(len,map(set,zip(*S))))>1,date.today().year in sorted(set(T))[1:-1])
from datetime import*

Try it online!

Japt, 22 bytes

Takes input as a 2D-array of integers for the space dimensions and a 1D-array of integers for the years. Outputs 2 for space only, 1 for time only, 3 for both and 0 for neither.

yâ mÊeÉ Ñ+!Jõ kVmgKi¹Ê

Try it

                           :Implicit input of 2D-array U=space and array V=time
y                          :Transpose U
 â                         :Deduplicate columns
   m                       :Map
    Ê                      :  Lengths
     e                     :All truthy (not 0) when
      É                    :  1 is subtracted
        Ñ                  :Multiply by 2
           J               :-1
            õ              :Range [-1,1]
              k            :Remove all the elements present in
               Vm          :  Map V
                 g         :    Signs of difference with
                  Ki       :    The current year
                    ¹      :End removal
                     Ê     :Length
         +!                :Negate and add first result