Ok.
Koine Greek (/ˈkɔɪniː/ or /ˈkɔɪneɪ/; from κοινός/κοινή "common", also known as Alexandrian dialect, common Attic or Hellenistic Greek) was the common supra-regional form of Greek spoken and written during Hellenistic and Roman antiquity. It developed through the spread of Greek following the conquests of Alexander the Great in the 4th century BC, and served as the common lingua franca of much of the Mediterranean region and the Middle East during the following centuries. [Bubenik, V. (2007). "The rise of Koiné". In A. F. Christidis. A history of Ancient Greek: from the beginnings to late antiquity. Cambridge: University Press. pp. 342345.]
The mainstream consensus is that the New Testament was written in a form of Koine Greek ,which was the common language of the Eastern Mediterranean from the Conquests of Alexander the Great (335323 BC) until the evolution of Byzantine Greek [Wenham The elements of New Testament Greek -p xxv Jeremy Duff, John William Wenham - 2005] [Daniel B. Wallace Greek Grammar Beyond the Basics: An Exegetical Syntax of the New Testament 1997]
Greek was the most ideally adapted linguistic medium for the World-Wide communication of the Gospel in the entire region of the eastern Mediterranean, Egypt and the Near East. [Archer, Gleason L. 1975. Zondervan Pictorial Encyclopedia of the Bible. Vol. 3. Merrill C. Tenney, ed. Grand Rapids, MI: Zondervan.]
Saying Koine Greek was the common language in "much of the Mediterranean" area stops well short of saying it was the primary language spoken in the region of Nazareth and Galilee. And it certainly doesn't make the claim it was the language spoken by Jesus and the disciples.
If you're going to contend that Jesus primarily spoke Koine Greek to the disciples, you need a credible source saying "Jesus spoke primarily Koine Greek to the disciples." You know, a clear an affirmative statement like this:
"It is generally agreed that Jesus and his disciples primarily spoke Aramaic, the common language of Judea in the first century AD, most likely a Galilean dialect distinguishable from that of Jerusalem.[1] The towns of Nazareth and Capernaum in Galilee, where Jesus spent most of his time, were Aramaic-speaking communities.[2]"
A source that says merely it was the primary language in other parts around the Meditteranean and Middle East doesn't get you there.