When they are streaming is it transcoding?

If not, it should be reducing the stream quality to adjust to the available bandwidth.

If it is, it could be limited to your pc’s available resources. You may want to turn on hardware transcoding.

Jellyfin has logs that will tell you if its transcoding and how well it’s working.

Tailscale does add additional hops to their route and has bandwidth limitations but it should be fine for streaming.

Tailscale can use relays if it cant find a way to make a p2p connection. Check the documentation. There is a command you can run to see whats using the relay.

If both your Jellyfin server and your siblings are behind residential CGNAT, then high chance your connections are relayed through Tailscale's DERP servers. You can check with tailscale ping-ing your sibilings' nodes.

If this is the case, you may consider selfhosting your own DERP somewhere close to you, but I'd argue the performance gains are minimal compared to the extra costs. Another solution would be to enable IPv6 for both you and your siblings, skipping NAT traversal. I just hope both ISPs support it and support it properly in $CURRENT_YEAR.

This is all assuming you can direct play (i.e. not transcoding) your media. If you're transcoding, then it's good to look into hardware acceleration like the other comment mentioned, too

If it’s cable internet you might just be constrained by the available upload speed. I tend to put my media in Storj then run a VPS somewhere between all the clients that serves the media via WebDAV with rclone. This gets around the slow upload speed of cable internet at home, and I can cache the remote content on my NAS at home too.

1. You might want to set an appropriate bitrate and video quality for transcoding for these users that works acceptably for their latency and bandwidth.
2. The reason netflix, prime, Disney+, etc work as well as they do is because they have CDN peering, so your version of Game of Thrones comes from somewhere much closer to you in a network sense. You can change your tailscale relay, or you can lock down jellyfin to their ip and specific port and skip the tailscale (I don't recommend it unless you know what you're doing) and let routing tables help with latency.

Before anything, are you doing regular restarts on your server? I had a similar issue (nobody overseas though) and they went away after restarting. So now I restart every few days to avoid any issues

All the answers so far could point in the right direction. I'm lurking to see which one pans out.

Jellyfin has setting for transcoding video when you are streaming to an external client. The problem is when you're using tail scale Jellyfin is seeing that client as internal. Because of this you must set caps on the bitrate within the client that is accessing via tailscale.

This of course is assuming your server is capable of the needed transcoding demands.