The O.E.D. gives the following entry for "Roman candle, n.":
- A cylindrical firework which discharges an upward stream or fountain of coloured sparks, stars, or the like.
1769 Public Advertiser 19 July 1/2 The Order of Firing..18. A Piece called The Fort with brilliant Fountains, Roman Candles, and Chinese Fires.
1784 London Mag. May 375/2 The manner of its bursting greatly resembled that of a fire-work, known by the name of a Roman candle abroad.
1799 F. T. Burton Artist's Arcanum 203 To charge the roman candles, Take half a tea-spoonful of corn powder, and then a star, and then two tea-spoonfuls of the composition, then a star, and so on alternately until the charge is complete.
1834 F. Marryat Peter Simple I. ix. 117 There were silver stars and golden stars, blue lights and Catherine-wheels,..Grecian-fires and Roman-candles.
1859 F. A. Griffiths Artillerist's Man. (1861) 280 The signal rocket stars are also the best for Roman candles.
1909 Westm. Gaz. 28 July 2/1 The use or abuse of Roman candles, paper-caps, display pieces, small crackers, or..torpedoes.
1956 R. P. Blackmur Anni Mirabiles 10 New talents were flung off like sparks from a Catharine wheel or the blobs of light from a roman candle.
2006 Vancouver (Brit. Columbia) Province (Nexis) 8 Sept. a13 Traditional fireworks like the burning schoolhouse, fountains, golden rain, lawn lights, pinwheels, Roman candles and sparklers.
This doesn't really help us very much, but the fact that the name arises so late suggests that the popular folk etymology that ascribes the name to emperor Nero's burning at the stake of Christians, is probably a delightful bit of marketing. Like so much in the naming of fireworks, I think it's probably just marketing to make them sound exotic and "highbrow" to an English-speaking audience. That the earliest quote, from 1769, mentions in the same sentence, "Chinese Fire", and the later quote "Grecian-fires", supports this reading.