From observation it appears that each instance that shows a quote to it's users needs to request permission from the source instance. This can take a while (my instance hasn't received it yet for a quote made nearly 30mins ago). It just shows "This post is pending approval...."
This poses 2 issues that I can see at the moment
1. By the time it's approved it's out of sight/mind
2. If a popular person quotes somebody can it DDoS their instance?