The two prisoners involved were the same inmates who Burns said caused "unrest" last week.
Specialist riot control teams were called on Monday night last week, after the first episode in the pair's fight to cohabitate.
"Two prisoners who were in an intimate relationship, and who wanted to be placed in a unit together, have been at the centre of the unrest," Burns said.
"[They] had made it clear they would create as much disruption as possible until they got their way."
Burns told the Herald last week the prisoners remained in separate units.
Heightened tensions at the prison also resulted in a transgender prisoner being transferred from the women's prison back to a men's prison.
The prisoner had identified as female and been approved to be placed in a women's prison since 2016.
Burns said the prisoner had been smashing windows and inciting violence in other prisoners.
The commissioner said last night's fire had been referred to police and a full review would be undertaken.
"The prisoners who started the fires will be held to account for their actions," she said.