Why would we want to join their empire?
We just met them. We don't know anything about them. We only know that they are technological advanced. We don't know if their morals/ethics are compatible with us. We don't know if they would even want us to join their empire, even if we were as far developed as they are.
There is multiple ways this can go. They might be conquerors and simply might want to take our resources. Look at Independence day. Not necessarily the most interesting story to tell.
Lets say they aren't outright hostile. But they aren't a charity, either. So make them interested in information. They probably want to study us, want to learn about us and the creatures living on our planet. After some negotiations, it is decided that they create an embassy on Earth, and that we keep an open communication channel with them. They send some scientists as well to study Earth. We will want to do the same with them. Maybe they won't hand us their technology, but information about their social structures, their home planet, their political landscape etc. are all very valuable.
This process will also yield information about what we have and they want and vice-versa. The first thing that happens is trade. Art in particular. Life will have developed differently on different planets, so there will be plants, tress etc. They don't know about. Those can be used as material in art they might be interested in. Music and instruments are another thing we might have to offer that they might want to import.
So at first, the relationship will be based on information interchange, then more and more trade. While art and entertainment always work, you could always make some resources restricted for them.
They might live on a quite barren planet and consider large bodies of water to be quite are. Earth could become a place of interest for tourism for them.
At that point we'd have a pretty good relationship with them. We interchange information and we trade. So we revisit the question I posed earlier:
Why would we want to join their empire?
On earth, nations trade and exchange information. Yet they rarely want to merge.
Maybe trading could be made easier if we were part of their empire. This isn't a problem we could negotiate a free trading agreement with them (think TTIP).
As long as there isn't an outside force / a threat, there would be no reason for us to want to join them in the first place. And even if there was another civilization that indeed was hostile, we still wouldn't necessarily want to join them. They could agree to protect us if they think relations are good, and might even try to ally with us (think NATO), because they might be interested in their enemy conquering a nearby star-system and would like the heads-up and warning. So much like NATO has less powerful members as buffer-zones, we could be a buffer zone for them and be under their protection.
In order for us to want to join their empire, there has to be a sense of common shared identity. Which needs to evolve over time, possibly generations. Nations on Earth form because of a long history and a common shared identity, the sense of "belonging together". This sense isn't just there.
So the question isn#t really what we can offer them in forms of trade/tech/knowledge, but the question is what can we experience together with them / what events might transpire to form a bond of trust, understanding and to create a shared identity so that we and them would want to merge into one empire. Its an interesting thing to explore.