Thats really weird. Since we have tried in multiple systems and have not been able to reproduce it to work in first try even once!
We have tried multiple browsers also.
Anything else we can try?
Can you please share your screen recording ??
@patrick I know you guys are taking a break, but it would be great if you could share your recording of how its working on your system.
We have tried a lot and its not working.
We recreated this test project today and restructured the logic on client & server side a bit.
Sockets now seem to be working without having to refresh the page; with session and changing team id etc. configured as per our basic requirements. 
Although, we realised by the end of it that the current implementation sends/updates data for all clients as noted by @s.alpaslan in another post. This means we need to wait for the update which would allow us to send information selectively - rooms & broadcasts as Serhat notes.
As @George confirmed, this is coming soon. Hope this in the pipeline to be delivered soon.
Keeping this post open just in case we run into any issues again with the newer update, when it arrives.