Not really. Once your tank has completed it's initial cycle you should not be able to measure detectable amounts of Ammonia or Nitrite. If you suddenly add a big bio-load then you may for a while, until the bacteria population expands to consume the new nutrients, but apart from that, this should not happen.
You don't have a problem however, just need to be a little more patient. What you are looking for is initially high Ammonia, followed by Ammonia lowering and Nitrites increasing, followed by Nitrites decreasing and Nitrates increasing. Once you can see Nitrates then you know your cycle is nearly complete. It is complete when the only measurable one of the three is Nitrates.
Here is what happened in my 65g tank when I first set it up as an example.
Day 1 filled tank, added salt, let it settle.
Day 2 added live rock (20 kg). Didn't bother to test as I knew the cycle would take time.
Day 7 added 3 kg more live rock (just additional aquascaping). Added bacteria in a bottle (Bactimax in this case). Tested later in the day, Ammonia 0.25 ppm, Nitrites 5 ppm, Nitrates 1 ppm. I considered this a very quick initial cycle but I did start with a lot of good quality live rock.
Day 9. Ammonia 0.25 ppm, Nitrites 3 ppm, Nitrates 10 ppm. Cycle now fully established and working.
Day 11. Ammonia 0 ppm, Nitrites 0.25 ppm, Nitrates 3ppm. Cycle nearly complete.
Day 14. Ammonia 0 ppm, Nitrites 0 ppm, Nitrates 0 ppm. Cycle complete.
My Nitrates did drop but that is not always the case. I don't understand enough about Nitrate consumption to explain my tank's behaviour - have a few ideas but nothing solid enough I am prepared to share!
The point is that you want to see the cycle progress through these three compounds. If you are left with Nitrates, that is fine and there are ways to manage that, starting with WCs.
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