Sounds like you didn't press "start streaming" in your OBS and only did "start recording"
You can link them to auto record when you stream in your OBS general settings. Then you only have to press one Start button instead of two.
You can also use plugins for your OBS rig that do automated recording on and off, scene switching, overlay triggering, all the basic and typical streaming things.
Plenty of how-tos on the web for streaming. All you need from HiveStreams is your streaming server URL and key from your hivestreams channel settings page. It even has pictures on it labelled to show you exactly what do to. ;)
Also as I mentioned in the comment on my post, you are welcome to join the discord for HiveStreams and find aid from the streamers hanging out in there, they are starting to arrive since I opened that up and linked it to the site too yesterday.
RE: A HiveStreams fail...