There is no direct proof of the substance behind the threat (if there even was any). However, we can still speculate.
Note that I don't believe it was the Second Sons. First of all, they are outnumbered by the Unsullied, and the masters would not consider a bunch of sellswords as their friends.
1. It was an empty threat
I wouldn't put it past them to threaten something that they cannot follow up on. Daenerys is considered naive after all, and before Tyrion, most of her (political) advisors weren't considered that experienced either.
2. They are referring to their friends, the other masters
The masters in general seem to be relatively well coordinated among themselves. They could simply be referencing the other masters, assuming that Daenerys would not be capable of standing up to an alliance of the masters.
They could also be referencing another major player, who operates on a slightly higher level than the master of Yunkai. If I'm not mistaken, Qarth was considered on a higher level than the masters of Yunkai (deeper pockets, more influence). Maybe it's Qarth, or a similarly powerful city.
3. They are referring to a Westerosi partner.
Robert Baratheon had kept an eye on Daenerys (via Jorah). We've seen other instances of the throne (King's Landing) being aware of Daenerys' current state. It stands to reason that they have spies abroad to follow up on Daenerys.
It's possible they talked to the masters of Yunkai, as I would expect the masters to be the easiest to contact from abroad. Plus, they are merchants, so they should happily render services (spying) for money.
4. They have a currently unknown partner.
This is of course nothing but speculation, but it is possible that there is another big player who has not been identified yet in the story. Maybe they were waiting for Daenerys to leave for Westeros. Maybe they are a major plot point near the end of the story.
I doubt it, but it's not impossible.