I have encountered similar glitches as you describe in A-Map 1.92 while hacking Emerald version. It appears that even after applying my Emerald Stabilization/0xFF patch, A-Map insists on overwriting music data higher up in the ROM (around the 0x6DXXXX area IIRC).
Since you don't mention which ROM you are hacking, I'll just assume it is Emerald. The solution I have found to this is to use A-Map 1.95 specifically when adding new Wild Pokémon data to a map. I think you'll also have to edit the program's main .INI file to search out the correct space if you are using Emerald, from 0x9C0B20 and onward (except a few parts which I mention in my tutorial). After doing this, I have not encountered any more glitches when inserting new Wild Pokémon data.
Now if you are hacking FireRed, Ruby, etc., I'm not sure what to tell you besides give A-Map 1.95 a try. Just don't use it for everything, as it seems to be quite buggy compared to 1.92. It's just that when it comes to creating new Wild data and Tilesets, it is the best choice in my experience. Good luck.