For me (I've only romanced Cullen and Solas so far - working on Iron Bull and Blackwall next), I had talked to Solas and Cullen while I was searching through the palace.
For Solas - it was the option to ask him to dance with you, he declines saying it would probably cause a fuss and he came out to my character at the end and asked her to dance.
For Cullen - it was the option to ask him to save you a dance. He tells you that he doesn't dance due to Templars not being trained and he came out to my character at the end and asked her to dance.
Thinking back on it...my Lavellan had flirted with Cassandra & Solas and was in a romance with Solas.
For Cullen - my Trevelyan had flirted with Josephine once, flirted a few times at the beginning with Iron Bull and was in a romance with Cullen.
I'm not sure what the triggers are - I will see how it goes with Blackwall and Iron Bull (Should be interesting...)