Eagle got it fairly right. There are two levels to focus on for NH3-, where 05 ppm is the big red line and .02 ppm or less is safe for quite some time. And NH4 which is way less harmful. How much is in each form in any tank depends on the pH and the water temp. So, you test with your API kit and then calculate from there, its a complex formula but luckily there are tables and calculators on the net to do the work. Here is the one I use which allows for both fw and to sw tanks. It should be noted that even if one's ammonia reading were to be all in the NH4 form (typical at a pH under 6.5), this may still harm fish at higher levels or if exposure is persistant rather than short term.
http/www.hamzasreef.com/Contents/Calculators/FreeAmmonia.php
When you use it do the following:
1. Select for the NH (NH3 + NH4) with the API kits. Do not select the one that has the -N after each term. This is a different scale and is used for different kits.
2. For fw tanks set the salinity to 0.
3. Enter your tank pH. (You posted it as 7.6)
3. Enter the temp of your tank water and select C or F.
4. Click on calculate and read the number that comes up for NH3 Concentration.
At pH 7.6, and a tank temp. of 25.5C (I had to estimate that since you did not report yours) and a reading of .25 ppm as you listed, the amount of NH3 in your tanks is .0059 ppm so you are .0141 under the danger line. You tank is safe for fish for quite a while assuming that level eventually goes away.
Because this is "New" tank where most of the old tank contents went in, most of the bacteria went in as well, But not quite all of it. So you may have a small reading. This should not be an issue at the level you gave.
Nitrite is a different story. Unlike ammonia, which in terms of cycling should not be neutralized, nitrite is easy to fight with the addition of chloride to the water. 2/3 of table salt is chloride so basically a small amount of salt in the water will block the nitrite from being taking in by fish. However, .25 ppm of ammonia can only produce .65 ppm of nitrite and that isn't bad for a short term either. I would expect your current reading of ,25 ppm to be gone overnight if it is a real reading (test kits are not so accurate at low numbers). The same will happen if small nitrite shows up.