As you note, the answers to this question will depend on the specific period of Roman civilization. Roughly, Latin fluency would be more common among higher social classes, more common in the West, and more common in earlier periods of the Empire. Latin was the language of command, and therefore normal soldiers would be able to understand it to that level, even if they didn't speak it otherwise.
We have archaeological evidence of military graffiti in Latin from various parts of the Empire - for example, in the second century, soldiers stationed at Hadrian's Wall were writing in Latin, as were others in Syria. The Syrian example also demonstrates graffiti in Greek and in a mixture of those languages. Since these texts are direct and unofficial, they are pretty good indicators of day-to-day military life. (Compared to seeing a tombstone in Latin - that's evidence of its official use more than its everyday use.) The actual examples of the language are dominated by personal names, or the names of legions and other units, but do include fragments of identifiable Latin grammar. So in this period, soldiers were writing short Latin phrases and expecting them to be understood - whether because they had it as a cradle tongue, or because it was a common language for soldiers of varied origins.
This matches with scholarly accounts based on Roman military writing, including those from much later periods (6th C. and later), where the general picture is that Latin was used for:
- many technical military terms (plus a little Greek)
- verbal tactical orders
- official bureaucratic writings
Broadly, this would enable Latin-speaking commanders to be understood by individual soldiers. But at that time, Latin was no longer a conversational language for most people in the East - they typically spoke Greek, even in the most elevated strata of society, and even for official purposes. The Strategikon, a military manual of the 6th C., notes that
a good number of Latin terms and other expressions in ordinary military use have been employed to make it easier to understand the subject matter
and gives examples of disciplinary formulae which were intended to be read out in both Latin and Greek. That all points to a world where one could no longer assume soldiers understood enough Latin to make sense of "don't run off and plunder the dead or you will be executed", but where Latin words and phrases were still normal for specific technical purposes and stereotyped commands ("attack now!").