"Chasing" each other can mean different things to different people. As someone mentioned, characins (the tetra species) are shoaling fish (live in large groups) and they interact within the group. "Play" may be a good description, or it may be spawning behaviour, or it may be aggression (mild or worse), all of which is perfectly normal.
If they are actually physically biting each other and tearing off bits of fin or scales, that is quite a different matter and not normal for this species. However, toward the Betta it is normal--pixielou85, I replied to that issue in your other thread so won't repeat all that here.
In a suitable environment (plants and bogwood are very suitable) the non-aggressive behaviour is normal and good to see, as it means they are "settled" and thus healthy. In this case, if the more aggressive behaviour is noted, it could be the small space; 10g is not much room even for 8 neons that should attain 1.5-plus inches. A 15 or 20g tank at 24 inches in length would be better if you can think down the road to something like that. Have a look at the info in our profile, click on the shaded name Paracheirodon innesi or Neon Tetra to see the profile.