Regarding the New Living Translation (NLT), Wikipedia states that it "was based on the two standard editions of the Greek New Testament (the UBS 4th revised edition and the Nestle-Aland Novum Testamentum Graece 27th edition)."
Regarding the New International Version (NIV), Wikipedia states, "The manuscript base for the New Testament was the Koine Greek language editions of the United Bible Societies and of Nestle-Aland."
Regarding the English Standard Version (ESV), Wikipedia states, "NT: 83% correspondence to Nestle-Aland Novum Testamentum Graece 27th edition."
Therefore, it seems that these three English versions rely heavily on UBS4/ NA27 eclectic manuscripts.
NA27 (personal copy)
Ἤκουσεν δὲ Ἡρῴδης ὁ τετραάρχης τὰ γινόμενα πάντα καὶ διηπόρει διὰ τὸ λέγεσθαι ὑπό τινων ὅτι Ἰωάννης ἠγέρθη ἐκ νεκρῶν
Ἤκουσεν δὲ Ἡρῴδης ὁ τετραάρχης τὰ γινόμενα πάντα καὶ διηπόρει διὰ τὸ λέγεσθαι ὑπό τινων ὅτι Ἰωάννης ἠγέρθη ἐκ νεκρῶν,
Ἤκουσεν δὲ Ἡρῴδης ὁ τετράρχης τὰ γινόμενα ὑπ᾽ αὐτοῦ πάντα καὶ διηπόρει διὰ τὸ λέγεσθαι ὑπό τινων ὅτι Ἰωάννης ἐγήγερται ἐκ νεκρῶν
This is a bit odd, but it seems that the NLT decided to rely more on the Textus Receptus in this particular instance, as the Textus Receptus has ὑπ᾽ αὐτοῦ, "by him," which presumably could only be referring to the singular Jesus rather than the plural apostles.
Constantin Tischendorf's critical apparatus:
Each variant, i.e. the omission and the inclusion of ὑπ᾽ αὐτοῦ, have significant witnesses. Nor is it easy to discern according to the context. The immediate context indicates that the apostles were healing the sick and exorcising demons (Luke 9:1-2). However, in the preceding chapter, Jesus performed many miracles, including healing the woman with the issue of blood (Luke 8:44), resurrecting the maiden (Luke 8:55), and exorcising the legion of demons (Luke 8:30).
Personally, I consider ὑπ᾽ αὐτοῦ to be more probable because Herod mentions the notion of John the Baptist being raised from the dead, as though he was the one performing the miracles. Thus, there's the idea of Herod hearing about a single man performing the miracles (he thinks it could be John, but it's Jesus). Again, although Jesus is not performing miracles in the beginning of Luke 9, he does perform many miracles in the immediately preceding chapters.