Your example is indeed problematic. The rule is to use an apostrophe in plurals only when you absolutely need it to remove ambiguity. This includes plurals like s's and pi's, but not requiems.
In your example, puto quis could be read to include the Latin word quis—which also exists, as you probably know—instead of qui. If the phrase puto qui is sufficiently well known and available to your audience, you might not need the apostrophe; but my choice would certainly be to use one to prevent ambiguity.
With italicized words or phrases that are pluralized without apostrophe, I believe some would italicize all but the plural s, as you did—but only if the same s could not normally be used to inflect the word or phrase, as it could in soirées. This use of a roman s would include the plural s used with acronyms or separate letters and that used with words or phrases where it is not or could not be a part of the word or phrase, e.g. where it could not normally be used to pluralize the word in the foreign language it came from. This would include your example and requiem, because the latter is in the accusative and short for a phrase, Requiem aeternam dona eis, Domine ("grant them eternal rest, O Lord").
However, I do not think this roman s is standard practice; I can't find a reference, but, unless used with an apostrophe, I'd recommend italicizing the s as well. I believe this is what most publishers would do. Whichever the case, any contrast between the italicized part and the roman s would be too inconspicuous to remove potential ambiguity. If an apostrophe is used, I think the s is generally not italicised.
Another reason to italicize is that there isn't always enough space to accommodate roman and italic letters so close together. This page won't allow it, but imagine what an italic g looks like directly followed by a roman s: the letters would get entangled in some fonts.