The family arrived on Scotland’s only major international flight arrival of the day – a Turkish Airlines flight from Istanbul that landed around 11am.
It is understood just four passengers travelled on the flight, including the family. The only other passenger was initially thought to be a sailor and exempt but on arrival it was discovered he had to isolate.
The flight initially had 65 people due to travel on it, but was delayed after 61 passengers decided not to travel.
It is not clear why they decided not to travel, but there are concerns about when the guidance from the Scottish Government was actually handed to airlines and whether the passengers plan on travelling to Scotland via England or Ireland.
Concerns about passengers avoiding the rules were raised by the aviation sector at the outset of the policy being announced by transport secretary Michael Matheson last week due to the potential for passengers to travel to Scotland on domestic flights and avoid the measures.
Airports have raised concerns on the voluntary nature of the policy for those arriving from within the Common Travel Area, likening the rules to the previous quarantine rules which required self-compliance by travellers.
Passengers arriving internationally to non-Scottish airports are only required to isolate if they arrive from a ‘red list' of 33 countries and only have to quarantine in hotels on arrival to Scotland if they voluntarily come forward.
Mr Matheson said on Sunday the loophole could “potentially undermine the public health approach here in Scotland” and described it as “unacceptable”.
The first passenger to enter managed isolation on Monday was a man and his daughter arriving from the USA via Dublin who voluntarily came forward at the airport.
Security firm G4S has been hired to undertake the majority of the work connected with the policy at airports across Scotland and are in charge of escorting passengers from the border to their hotels.
In Edinburgh Airport, passengers arriving internationally will have filled out their passenger locator form pre-departure, which will state whether they need to quarantine or are exempt.
Border Force staff checking those forms will then flag individuals to G4S staff who escort travellers to a waiting area before passengers are allowed to pick up their luggage.
From there, travellers are escorted to a bus where they are transported to the DoubleTree hotel near Edinburgh Airport, which is currently being used to house incoming travellers.
However, due to the lack of security clearance – a process that normally takes six weeks – airport staff must escort the security staff around the airport throughout the day.
Aberdeen Airport is the busiest international airport in Scotland today due to having two flights arriving from Norway, one from Bergen operated by Wideroe airlines and one from Stavanger operated by Scandinavian Airlines.
However, the majority of passengers arriving on those flights are understood to be oil and gas workers who are exempt from the requirement to quarantine under current rules.
Glasgow Airport has no international flights today, but has staff in place should someone come forward requiring to quarantine on a connecting flight.