sync issues?

I established syncing between PC and phone, and it seems that what I receive from others, I get it into both devices.

However what I send from one device, doesn’t get synced into to the other, :( Is this an issue? I was hoping what I do on one device gets reflected in the other, and in the right order...

Also, when I send messages to myself in one device, the other device doesn’t get it, :(

Same seems to happen with invitations. If I get an invitation in one device and accept it, the other doesn’t realize about it, and have to accept it as well separately…

Finally, when syncing between devices is enabled, only new communication from others, from that point on, gets synced. Prior communications aren't synced at all. It seems like an issue to me, but the prior ones seem relatively more important...