Yes, ammonia is only converted to nitrite, never directly to nitrate. So for you to have high ammonia, no nitrite, and a reading for nitrate indicates that you have aa full cycle, but its getting backed up at the first stage...nitrite is being consumed as fast as it is produced.
First ammonia must be ppresent, then bacteria colonize and convert it to nitrite. After nitrite rises, another type of bacteria converts it to nitrate. Because you had very high ammonia and you are getting a reading for nitrate, you probaly have been colonized by both types of bacteria. Now that you have lowered your ammonia, the bacteria colony is consuming all of the nitrite that is being produced and turning it into nitrate faster than ammonia is being turned into nitrite.
It is rare to see ammonia remain high while nitrite is being efficiently processed so watch out for nitrite spike once the ammonia-consuming bacteria catch up. Your low ph may have somthing to do.with the ammonia remaining high, but usualy its the nitrite-consuming bacteria the have a hard time in acid water(pH below 7.0)
Sorry if this is confusing- I'm up at 4am due to insomnia and I just cant seem to simplify it in writing right now.
Thanks for posting your test results, this can be a learning oppurtunity for all of us.