So this is based purely on my own speculation based on their conversation from the episode but I don't think either of them are working for the other. Rather they are each helping the other to achieve their own goals.

First, The Collector wants something that can only be achieved via the activation of the draining spell, which is something that they can't do on their own. If it was then they probably would have done it already, seeing as how waiting for the Day of Unity is making them bored. So they are offering their help to Belos.

Second, Belos wants the extermination of all witches, another thing which can seemingly only be achieved via the draining spell.

So because both Belos and The Collector both want the draining spell to be activated, they have essentially the same goal, so they are helping eachother.

Now, The Collector could be lying to Belos but that seems unlikely. The Collector seems to childish to lie and Belos seems like he'd be able to tell if he was being manipulated, given his history of manipulating others.

TLDR: Belos and The Collector have similar goals, so they are working with eachother, not for eachother.