I got all 4 mons before doing the transmission quest you get after the first mon. I just did that quest but I haven't been able to trigger another transmission. Did I break my game?

I don't know, but the thing you should try to trigger a new transmission is to travel between several different areas. But don't do it quickly... travel to one of the areas, wander around for a little while, then go somewhere else, wander for a while, etc. It can take some time for the transmissions to trigger.

But when I played I did the transmission quests as soon as they came up, so I don't know if it breaks the game to do it the way you did. Anyone else know?

I got the first mon in Shamazaar and have been exploring Talanzaar for quite some time but still haven't gotten the first transmission from the girl (I forget her name). Is this normal? I remember getting the transmission while I was still looking for the mon back in the day (granted this was over 10 years ago so I could be way off).

The very first transmission will tell you to go to Talanzaar, so I think you can only receive it if you are not already there. Try going to a different area and wandering around for a bit.

My memory is that I got the transmission as soon as I found the first Mon, but other transmissions took a little while to trigger so I'm not sure whether that always happens.