The nock should be just tight enough that the arrow can dangle from the string without falling off. If you tap the string, it should make the arrow fall off.
If the nock is too tight, arrow flight won't be as good as if the nock has a correct fit.
If my nocks are too tight, I hold them in boiling water for about a half minute to soften the plastic a little, and then press fit the nock over a piece of copper wire I found that will give me the correct fit. I just snap it on and immediately off the wire, without holding it in place, and then the nock fits my string perfectly. You just need to find something like my piece of copper wire that will give you the correct fit.
If my nocks are too loose, I just hold them in boiling water, and then squeeze the ends together a little.
If you try to adjust the nock fit when the nocks are cold, by biting the ends of the nock, for example, you risk fracturing the plastic and weakening the nock. Filing is okay, but time consuming.