Hebrew was still a spoken language
Ancient Greek had a word to refer to Aramaic: Suristi. This word never appears in the New Testament. Since they could have referred to Aramaic if they wanted to, but never did, that would tend to support the view that when they say Hebrew they mean Hebrew.
Hebrew shows up in many places in late second temple Judaism, and not just in copying previously-written ancient Hebrew documents, but in additional writings in the Dead Sea Scrolls, letters, coins, and numerous Jewish teachings & commentaries. (drawn from a much more detailed discussion by Frank Luke on this site here)
For a summary discussion of the presence of Aramaic, Greek, and Hebrew as spoken languages in the time and place where Jesus lived, I provided some thoughts on this site here.
For a sharp critique of the theory that spoken Hebrew no longer existed in Jesus' time (and how that theory developed), see here. The idea that Hebrew was not spoken is oft-repeated but rarely argued from evidence.
Ἑβραΐδι διαλέκτῳ
Interpreting Ἑβραΐδι as "Aramaic" worked in a scholarly world that assumed Hebrew was not spoken. The evidence of a living Hebrew language (Mishnaic--see below) at the time of Jesus has invalidated the Aramaic interpretation.
In a region in which Aramaic, Greek, and Hebrew were spoken, "Ἑβραΐδι διαλέκτῳ" would be a plausible way to say "Hebrew", but would not be an effective way to disambiguate Aramaic.
Buth & Pierce have recently argued cogently that ἑβραϊστί and related words were never used to refer to Aramaic.
(see R. Buth and C. Pierce "Hebraisti in Ancient Texts: Does ἑβραϊστί Ever Mean 'Aramaic'?")
What about BDAG?
BDAG suggests that "Ἑβραΐδι" and related words refer to Aramaic. The aforementioned 2014 work by Buth & Pierce challenges the assumptions behind the consensus BDAG represents:
"The present study will investigate the claims of BDAG. It will be
shown that there is reliable, lexicographical, and contextual support
for the meaning "Hebrew language"...for the passages cited in BDAG. It
also will be shown that there is no methodologically sound support for
the meaning "Aramaic language". This is a classic example where a
priori assumptions have led a field to ignore the evidence and to
misread it." (ibid)
Biblical Hebrew vs Mishnaic Hebrew
It's worth clarifying that Hebrew, like any language, changes over time. It has frequently been noted that Biblical Hebrew was a dead language in the 1st century. Was it? Well, it was a dead language in the same sense we might say Shakespearean English is a dead language today. It's dead in that it isn't spoken colloquially. But it's not dead in the sense that it only exists in academic circles. Because some of the most influential English texts of all time (writings of Shakespeare himself, the King James Bible) were written in this dialect of English, the dialect is still understood by numerous English speakers today.
1st Century Biblical Hebrew appears to be in the same boat -- important writings like the Torah & Isaiah ensured that even though people didn't colloquially speak Biblical Hebrew, they understood it. This video presents a more extended form of this argument (disclaimer: I made this video).
The spoken Hebrew of the time was Mishnaic Hebrew, a descendent of Biblical Hebrew. For a discussion regarding the relationship between these dialects, see here and here. It's nuanced as all language development is--people didn't just stop speaking one and start speaking the other in an instant.
Conclusion
Although it was fashionable a century ago to argue that 1st century Galileans were monolingual (this may be why some modern translations gratuitously introduce the term "Aramaic" when the original Greek said "Hebrew"), more recent evidence has overturned this older theory.
If they could speak Hebrew, why be surprised when Acts says that someone spoke in Hebrew? Rather than read something into the text that isn't there, I would favor the most straightforward explanation: they say Hebrew because they mean Hebrew.
