It follows a mix-up over the weekend which saw a number of people arrive at the centre only to find no screening was taking place.
The mobile testing unit, which was based at Carrickfergus Rugby Club car park, was established in early August.
East Antrim MLA Stewart Dickson said the online booking system had allowed a number of people to make appointments at the site on Saturday and Sunday.
"Up until now [the test centre] at the car park had been very well organised," Mr Dickson said.
"The PHA have been organising testing, but outsourced the booking to a digital platform in London; tests in Northern Ireland have to be booked through the UK Government website.
"At the weekend, people were allocated tests on Saturday and Sunday, but when they arrived they found there was no-one there. One lady in particular had come all the way from Dungannon to the testing centre.
"It was a bit of a shambles."
The Alliance Party representative reported that some individuals were then redirected to a testing site in Antrim.
"I contacted the PHA and they did get back to me to apologise, and to make sure someone from the testing company was sent to the site to explain to people that they would not be screened there," he added.
"With kids being back at school and some having sniffles and colds, you have teachers recommending that they get tested; of course, there's the importance of testing for key workers as well. But if the PHA is going to engage with a national booking system, they need to make sure it's working correctly.
"It also needs to be communicated that these sites are 'do it yourself', self-testing sites rather than having a medical professional test you."
Mr Dickson said he would be submitting a priority question to Health Minister Robin Swann over the issue.
Meanwhile, a spokesperson for the Public Health Agency said the mobile testing unit previously located at Carrickfergus Rugby Club was moved to a new location at Antrim [Forum] on Saturday September 5.
"Unfortunately the Department of Health and Social Care (DHSC) portal for booking tests did not update the new location and incorrectly booked people for Carrickfergus after the mobile testing unit had moved," the spokesperson added.
"When we were made aware of the situation we worked with our colleagues in DHSC to ensure changes were made to the booking portal to reflect this.
"Anyone incorrectly directed to this location should log on to the testing portal and re-book a test if they have not yet done so."
Mobile testing units are short-term testing sites that are mobilised in response to need and/ or to provide additional testing capacity locally, the Agency said.
"They work in close collaboration with the four fixed sites located in Belfast, Enniskillen, Derry/ Londonderry and Craigavon," the spokesperson said.
"When a mobile testing unit is fully booked, members of the public are directed to another mobile testing unit or fixed site for their test. This helps ensure efficient use is made of our COVID-19 testing resources in Northern Ireland.
"Information on the location of mobile testing units is available on the PHA website."
A message from the Editor:
Thank you for reading this story on our website. While I have your attention, I also have an important request to make of you.
In order for us to continue to provide high quality and trusted local news on this free-to-read site, I am asking you to also please purchase a copy of our newspaper whenever you are able to do so.
Our journalists are highly trained and our content is independently regulated by IPSO to some of the most rigorous standards in the world. But being your eyes and ears comes at a price. So we need your support more than ever to buy our newspapers during this crisis.
With the coronavirus lockdown having a major impact on many of our local valued advertisers - and consequently the advertising that we receive - we are more reliant than ever on you helping us to provide you with news and information by buying a copy of our newspaper when you can safely.
You can also enjoy unlimited access to the best news from across Northern Ireland and the UK by subscribing to newsletter.co.uk
With a digital subscription, you can read more than five articles, see fewer ads, enjoy faster load times, and get access to exclusive newsletters and content. Visit https://www.newsletter.co.uk/subscriptions now to sign up.