You have to use all the information available to you, including the in-game appraisal system. Learn what the phrases your team leader uses mean, and use that information to help you narrow down the possibilities.
Take this Weedle as an example
If you enter in the information from this screen into the IV Calculator at Poké Assistant, you'll end up with 14 possibilities.
If you use the in-game appraisal, the team leader indicates that HP is the best stat, and that it's either 13 or 14. If you enter in that information, you'll only be left with 6 possibilities.
However, the team leader also said that the Pokémon was "decent" (team Valor), so you know the Pokémon must be between 51.1% - 64.4% perfect. This means that you can exclude the last four items that Poké Assistant listed, leaving you with only two possibilities.
From there you can further narrow the possibilities down by powering up the Pokémon, and entering the new values into the calculator. Using a second calculator can also help you narrow it down.
At any rate, the evaluation is based on the Pokémon level, not the trainer level. You can estimate the level of a Pokémon, by looking at the stardust required to power it up. In my example above, the Weedle must be either level 13 or 14, based on the stardust required to power it up.
To answer the question directly, the IVs don't change based on level. What an IV calculator is showing you, is all the possible IV combinations that would produce a Pokémon with the stats you entered.
In the above example, a level 13 Weedle with 5/0/14 IVs, and a level 13 Weedle with 0/10/14 IVs, both result in a level 13 Weedle with 131 CP and 45 HP. The only difference would be the IV distribution, and the percent perfection.