Mm, bacon, tasty!
I'd say that regardless of terminology, I'd want to know where I stand in any kind of relationship.
You definitely don't have to be at the mercy of the guy you're dating and his partner.
It's a tricky one - the whole thing about priorities of 'primary' partners is being debated over in another thread (entitled something like how quickly should you meet a lover's girlfriend, if you do want to check it out).
The guy you're dating will have his own set of priorities, whether he's single or partnered up. Since he's partnered up, it's likely that his existing relationship will be a current priority. You have to ask him about that and what he wants from your relationship.
To be fair: as for your lover needing to spend time with his primary... often when people live together, they don't get much quality time. It's all housework and cooking, perhaps children, work talk, one person on the computer and one person watching the TV. Often, you have to set aside a chunk of time to just 'be' together.
This is especially true if one, or both, partners has been freshly dating. New dating can be very time consuming and can be stressful for the other partner. For example, my girlfriend has just come out of a whirlwind of dating over the past two months. I've been dating a girl for about a month. Constant online chats with our dates, constant discussions about how we're both feeling, mild stress about new sexual partners, constant effort being put into NRE (New Relationship Energy) with the new people.
We finally got a chance to put everything aside, calm it all down and spend some time together and it was much needed.
So especially if your guy has just started dating you, he and his partner probably need a little 'refocus' time. That's a good thing - it tends to mean they know how to keep their relationship healthy
I'm not going to get into the whole secondary debate here (i.e. is a secondary less important), because it's being discussed on other threads and I don't want to stir things up.
Ultimately, you have to know what your own expectations and boundaries are.
I have a 'primary' partner, a girlfriend that I'm committed to, who is my priority. As for women that I date outside of our relationship.... I'm very happy not to be their top priority. In fact, I prefer it. I really don't mind fitting around their schedule if mine matches up. If I was single, I might find it harder - I don't know.
The most important thing is that you get your needs out there on the table.
Take the girl I recently started dating - she's new to poly too. We sat down and outlined what we both wanted. I basically said (in the kindest but most open way possible) - I am not looking to fall in love, I don't have the time or emotional capacity right now. I want friendship with benefits. I want casual. My girlfriend will come first for me, but I will always treat you with respect and kindness, listen to you and care for you as a person. If ever your feelings start becoming deeper than this, if you become upset, or want something else, please tell me.
That arrangement suits us. We can't promise that someone won't get hurt - but we've put it out there on the table and now it's just down to communication.
Can you tell us a little more about your situation? How long have you known your guy? Have you met in person? Have you met his partner? What is your relationship with him like? Do you have any examples of feeling at their mercy?