Robin Swann says officials remain in discussions with the Irish Government over how to manage the 14-day travel quarantine.
The Health Minister said details around cross-border issues are still being thrashed out - even though the controversial scheme went live this week.
From Monday anyone arriving into the UK is required to provide an address to self-isolate for 14 days.
Here, anyone refusing to provide passenger information risks a £60 fine.
The penalty is increased to £1,000 for those who leave self-isolation within the 14-day period.
However, exactly how the scheme will be policed is still unresolved.
Concerns have been raised about the monitoring of people who arrive into one jurisdiction from overseas and then travel across the border to get home.
On Monday the PSNI confirmed that Stormont had yet to set out the precise enforcement arrangements despite the rules already being in force.
Amid mounting criticism, First Minister Arlene Foster denied the rules were a waste of time. However, Deputy First Minister Michelle O'Neill acknowledged their complexities posed problems for police.
Yesterday Mr Swann said conversations had taken place between the Executive and the Irish Government.
Mr Swann said discussions were ongoing about getting "mutual signage" in place at airports and ports across the island informing passengers what the law was on the opposite side of the border. He stressed the rules people must place themselves under are those that apply in their place of residence, not their port of arrival.
Mr Swann said this would be made "very clear", adding: "If you land in Dublin and come to Northern Ireland, you're duty-bound under our regulations.
"If you land in Belfast and go south, you're duty-bound under their regulations, so it's about the sharing of that information so that when people arrive or pre-book their tickets, [in] the UK system you can make that application online two days before you fly.
"It's making sure that we have those information panels present and in all the Irish airports and ports as well, and that we mutually respect and support them in the utilisation of any Irish citizen who is landing in Northern Ireland." Separately, Stormont ministers have raised concerns with the Irish Government over a perceived lack of consultation on its lockdown exit plans.
The issue was discussed at a virtual meeting yesterday involving senior ministers from both administrations and Secretary of State Brandon Lewis. Mr Swann said the Executive was being made to look as if it should be "playing catch-up" with moves south of the border.
Taoiseach Leo Varadkar has said he and Tanaiste Simon Coveney did inform Stormont counterparts ahead of Friday's announcement on an acceleration of Ireland's roadmap to recovery.
But Mrs Foster and Mr Swann are among those to have voiced concerns about the extent of that consultation.
Mr Swann said he had raised it directly at the now regular cross-border political "quad call" earlier in the day.
The call involved Mr Coveney, Irish Health Minister Simon Harris, Mrs Foster, Mr Swann, Mrs O'Neill and Mr Lewis.
"Where they moved without giving us a lot of consultation as to their movements was raised," said Mr Swann.
"I raised it because it does put our Executive into a place where it seems that we should be playing catch-up, when in fact we're not.
"We were always clear from the start that our programme was not being date-led, it would be led by where the coronavirus was in Northern Ireland and where science is."
Mr Swann acknowledged it was for the Irish Government to make its own decisions on its lockdown plan.