The notion of a theme park for dolphins has met with strong opposition from expats living on the island, local university students and wildlife advocates around Thailand.
Backed by Russian businesspeople, the theme park is proceeding even though the Russian market of tourists to Phuket has since collapsed.
Numbers of Chinese, who are expected to provide most of the audience, have increased.
Progress of the flight bringing the dolphins is being tracked but details remain sketchy today.
According to the Facebook post at Phuket Says No to Dolphin Shows, ''Bottlenose dolphins transferred from the NEMO Odessa to Thailand on October 6, 2015.
''The number of dolphins transferred was not disclosed & according to the news the transport plane, IL-62, which carried dolphins in Thailand, made a stopover in Iran's Isfahan then disabled their transponder.''
Officials from Thailand's Fisheries Department said last month that the final hurdles to gaining permission for the dolphins to be brought to Phuket had been overcome.
The post at the Facebook protest site says: ''The Dolphins are on their way to Phuket. We all feel disgusted right now. Shame on Phuket. Please share and please help us try and educate everyone why buying a ticket is so very wrong.''
The post contained a link to a Russian site and the following information in translation: "Cargo IL-62M Airlines Belarusian Rada Airlines flew to pick up a certain number of dolphins for "Nemo" (LLC "Nerum") and deliver them to an Asian country.
''Transportation of dolphins - it is very troublesome, so for this purpose was chartered aircraft with long range, capable of non-stop to reach the destination. The price of this trip - not less than 100 thousand US dollars, reported the "Duma" sources at the airport.
''Dolphinarium Co-owner Andrew Kislovskiy confirmed the export of marine mammals from the Ukraine. According to him, the young Black Sea and Pacific dolphins were born in captivity.
''They are destined for the island of Phuket in Thailand, where "Nerum" recently completed construction of a new dolphinarium.
"As soon as the animals arrive, the venue will open," said the businessman.
He argues that "Nerum" has all the documents allowing the export of the creatures, including certification of the Ministry of Ecology and Natural Resources.''
The Dolphinarium is near Phuket Zoo, on the road to Palai on the island's east coast.
The Thai tourism organisation SKAL has also issued a media release and joined the protest against the planned opening of a dolphinarium on Phuket.
The protesters won Phuketwan's award for the most important environmental activity of 2014.