Can someone versed in open source licenses chime in in what it means to use this service since it is licensed under the AGPL? I'm not an expert but as I understand it AGPL can require your own code to come under AGPL as well?
No, it should prevent someone else taking the code and starting a competing service with said code without opening its source.
If it was GPL, you'd be forced to open your source if you distributed your software to others - it does not apply to a web service where the software is always ran in the owner's computer. So I could take your GPL code, build a service running on my server (without ever distributing the actual software) and not open my source. AGPL tries to fix that loophole.
So if you are a user of this service, license has nothing to do with your own project, you are just a user of the service. But if you grab the source and create your own analytics (or something else) service from it then you have to open that source even if it runs on your own server(s).