Universal Spooky Meme Translator

Ruby, 50 44 43 bytes

FGITW answer. Gotta go fast!

Thanks to @Neil for saving 6 bytes.

Oh right, crossed out 44 is still 44

->m,t{m.gsub(/\d+/){eval$&+t.sub(?^,'**')}}

Perl, 36 34 bytes

s/\d+/"0|$&$^I"=~s#\^#**#r/gee

The source code is 30 bytes long and it requires the switches -pi (+4 bytes). It takes the first input from STDIN, the second input as an argument to -i.

Thanks to @DenisIbaev for golfing off 2 bytes!

Test it on Ideone.

Jolf, 15 14 bytes

ρi«\d+»dC!6+HI

Try it here!

Explanation

ρi«\d+»dC!6+HI
ρ «\d+»         replace all digits
 i              in the input
       d        (functional replace)
         !6     eval (using jolf's custom infix eval)
           +H   the number as a string plus
             I  the second input
        C       floor the result (integer truncate)

---

Fun to note, I updated Jolf after this challenge, adding some RegExp builtins. This could be 12 11 bytes:

ρiLRdC!6+HI