The use of the common language is a red herring. In the end, a sentence formulated in the speaker's language has to be cast in the listener's language.
In the field of automated translation, this approach is called interlingual machine translation. The text in the source language to be translated is transformed into an interlingua, that is, either a pivot natural language or an abstract language-independent representation, and the text in the target language is then generated from the interlingua. Nowadays, this approach is used when automatically translating between languages for which the direct translation path is much less well developed than translation paths to and from a pivot language, quite often English.
Let's try Latin to English: the speaker formulates the sentence "hi omnes linguâ, institutis, legibus inter se differunt". The listener must hear "all these differ from each other in language, institutions, and laws".
The translator begins all these, but then must pause and wait until the lips or the mind of the speaker reach differunt because English absolutely wants a verb after the subject, and Latin (in normal prose) is very reluctant to put it there. The translation simply cannot continue until the Latin sentence reaches its verb, because the translator cannot look into the future, and the speaker may have wanted to say similes sunt (are similar)...
In practice, speakers who deliver a speech with simultaneous translation into one or more other languages, are instructed to keep their sentences as short as practicable and to pause after each sentence to allow the translators to translate. (In better venues, where simultaneous translation is often performed, the speaker's lectern may even feature a red and a green light, controlled by translators; the speaker speaks when the green light is on, and pauses when the red light is on.)
Or else, maybe the culture has evolved to be tolerant of Master Yoda-speak: after all, rendering
"interea eâ legione quam sécum habebat militibúsque, qui ex provinciâ convenerant, à lacu Lemanno, qui in flumen Rhodanum influit, ad montem Juram, qui fines Sequanorum ab Helvetiis dividit, milia passuum XVIIII murum in altitudinem pedum sedecim fossámque perducit"
"in the meantime, with the legion he had with him and with the soldiers who from the province had come, from lake Leman, which in the river Rhone flows, to mount Jura, which the borders of the Sequans from the Helvetians divides, a 19 miles wall, in height sixteen feet, and a ditch, he carries"
is sort-of intelligible, even if bad English.
(Of course, the correct translation would be
"in the meantime, with the legion he had with him and with the soldiers who had gathered from the area, he builds a wall 19 miles long and sixteen feet tall, and a ditch, from lake Leman, which flows in the river Rhone, to mount Jura, which separates the lands of the Sequans from the Helvetians".)
(Olde skoole English translations have "in the meantime ... he carries a wall" etc., but in contemporary English "he builds" is much better, as that particular usage of "to carry" is no longer in use.)
(For some strange reason, Lake Leman is most often called Lake Geneva in English, or so Wikipedia informs me. Dear native English speakers, that lake has a proper name, which has been in use for thousands of years.)
The examples are taken from Caesar's Commentaries on the War with the Gauls, which is written is a very straightforward and clear style, quite often being the first for-real Latin text assigned to beginners to parse and translate.
To preserve real-time communication a very much better idea is to have both the speaker and the listener actually learn the common language, possibly materialized in different phonetic or signalling forms. A person who actually knows a foreign language to any level better than first year beginner is perfectly able to think in the foreign language, and to follow a sentence in real time, without having to wait for all the pieces to come in so that they could cast it in their native language. The automatic mind-to-mind translator would still have to supply the meanings of common language words which the speaker or listener doesn't yet know, but that is comparatively much easier.