The first passengers to arrive at Edinburgh Airport on Monday and move into a quarantine hotel have been released already because they flew through Dublin Airport.
A flight from Dublin Airport to Scotland is confirmed to have been carrying American passengers.
Among the passengers were Chun Wong and eight-year-old daughter Kiernan who flew in from the US via Dublin Airport, and were sent straight to a hotel at Edinburgh Airport.
But Mr Wong said after less than a day in quarantine officials told them they had mistakenly been quarantined as they could self-isolate at home in Fife.
The pair were among the first international travellers to go into a quarantine hotel in Scotland following new quarantine rules on Monday.
In Scotland, only travellers coming in from overseas countries will be required to stay at one of six designated hotels in a bid to avoid importation of the virus, with Ireland exempt - although travellers from Ireland and other UK countries are still expected to self-isolate for ten days, Mirror.co.uk reports.
The loophole in the system means that those arriving from Dublin do not have to pay to enter a hotel because Ireland is being considered 'exempt' from the new rules.
Mr Wong and Kiernan are allowed to self-isolate at home.
Mr Wong told the BBC : "I received a call from reception saying a gentleman from the airport would like to talk to me.
"He said that since I landed in Dublin first and then got a connecting flight to here, I was not required to quarantine in a hotel. I still have to quarantine and do the self-testing kit on the second and eighth day, but they said it was an error on their part."
Mr Wong was told he was free to leave the hotel but as he was tired he stayed the night.
He said officials were making arrangements to transport him and his daughter to his home in Fife on Tuesday.
Mr Wong worked in healthcare in America and his family are moving to Scotland to be with Kiernan's mum and his wife Danielle.
Danielle, who is a dual UK/US citizen, has been in Scotland since November 2019 and is a front-line worker helping to care for people with addictions.
The family have been apart for 16 months and Mr Wong said the prospect of being apart for a further 10 days was "heartbreaking".
Mr Wong said after being told they didn't have to quarantine he was relieved while his daughter was "ecstatic, overjoyed and a little nervous" as it had been 16 months since she had seen her mum.
He is now hoping he will be given a refund for the fee he was forced to pay to quarantine.
