I agree with most of what the previous replies have added. On your end, you decide your timeline, not anyone else... period. You're a grown person and one of the great things about my personal poly outlook is that no one has any rights over my time/body/emotions... none whatsoever. If I have a care to accept a request to meet someone then I will do so, if I don't then I will not.
"Let's give it a bit more time" sounds like you are being quite reasonable. If their relationship demands that you have to meet her immediately then maybe it doesn't work out. You'll just need to decide that for yourself.
Personally I would find the entire discussion very off putting. I saw a profile on a dating site where the girl linked her boyfriend's profile and said that any suitors would need to talk to him before gaining access to her. Yeeeaaaah that's not going to work for me. I don't want to be involved in a relationship where anyone involved feels that they have the right to tell me what I need to do, when, or how. I'm looking for romance, not a new employer.