Stax, 26 26 24 bytes

ëks░Wa╛┐=/c'∙aß♣P└27_╟╖qj⌡Ç╕SôεPN^:·░ßⁿ {@ÿ}Ü╫╣1╣X

Run and debug itRun and debug it

Explanation

E{b+}99*L{E%2>|cd_E:-u%1=!C_Qf    # Full program, unpacked, implicit input
E                                 # Push all elements from array onto stack.
 {b+}99*L                         # Generate the first 99 numbers of the  Fibonacci sequence given the input
         {                   f    # Loop through all Fibonacci elements
          E                       # Array of decimal digit
           %2>                    # Does the array have at least 3 digits
              |c                  # Assume Truthy past this point
                d                 # discard top of stack
                 _E               # Copy the current element of the Fibonacci sequence and Digitize it
                  :-              # Pairwise difference of array.
                    :u             # Get unique numbers
                     %1=          # Is there exactly 1 unique number
                        !C        # Flip the comparison, if truthy proceed
                          _Q      # Copy the current element of the Fibonacci sequence and Peek and print with a newline.

Not as short as I would like it and can probably be golfed a bit more, but it works.