#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](https://ethproductions.github.io/japt/?v=1.4.6&code=eeIgbcplySDRKyFK9SBrVm1nS2m5yg==&input=W1s1LDcsMl0sWzUsMyw4XSxbLTYsMyw4XSxbNSw3LDJdXQpbMjAzOSwyMDE5LDIwMTgsMjAzOSwyMjIyXQ==)

                               :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