How can you tell that this visual pun was created by a north American? Because it doesn’t quite work in BrE or, therefore, in Australian/NZ/South African English.
Why not? First, and obviously, because in BrE barium has the stressed vowel eə while bury has e. So for us Brits barium sounds different from bury ‘em. But in AmE they are homophonous.
But secondly, I think, because we don’t use the form ’em for them as freely as Americans seem to. Our weak form of them is generally ðəm, with the initial consonant retained. As the OED (1891) comments under ’em,
The emphatic form of the pronoun was early superseded by THEM pron., but the unstressed form continued to be used, being regarded as an abbreviation of them. In literature it is now obs. or arch., but is still common in familiar speech.
Obsolete or archaic… yes, but not really "still common in familiar speech" (or so it seems to me). Rather, as far as I am concerned it seems to be generally restricted to a few set formulaic expressions such as If you can’t beat ‘em, join ‘em and give ‘em the money. Beyond that, them can lose (or assimilate) its ð in the same way as that, the or they when following z in phrases such as is that, was the, claims they, sees them.
When I was a small child we spent family holidays in a friend’s unimproved rural Yorkshire cottage called, for some reason, Buryemwick ‘Bury them alive’. But if asked what to do with dead cats, for example, we’d never have said “bury ‘em”, but rather “bury them”.
It would also be possible to take the final əm of barium as representing not ’em but him (‘im) — but only in an accent of English that has lost the contrast between ɪ and ə in this position, as in often the case in AmE but generally not the case in English English.