I would start by not so much calling it a "cutting phase" as much as clean up your diet - I'm assuming that you're starting from wherever your current 'lifestyle' has brought you as opposed to you doing an intended shitload for a while. At your age, you should be able to eat a lot and burn it up / build nicely. But depending on your regular metabolism, hormone levels, etc. you may be the type of person who builds both fat & muscle easily - so the result of an unstructured diet can be you buidlign muscle but getting a lot of fat with it. 20% bodyfat on a guy is a bit hefty relatively speaking. If you start bulking your just going to get fat.
Your trainer is right - one of the nice little upsides of depleting yourself down for contest prep is the anabolic rebound that follows - but the value of all of this will be much better if your dieting habits (i.e quality of food) are already in place and not just you following a "cutting" or "bulking" diet.
For craps & giggles can you post up your typical meal plan - I'd like to know what is 'normal' for you now - i.e how you got where you are now. You're still very young so a few minor adjustments and maybe (I'm assuming.. I dunno) a little more structure, discipline and focus on your goals instead of just being a guy your age and enjoying life, will get you some amazing results w/o even trying. Any additional training / dieting program you do will just optimize what you would have as your 'baseline' set of habits.
(Sorry for the ramble - just sitting here at my age now, and looking at a guy your age who wants to start going after particular results, one of the best things I can tell you is to establish some good eating habits as your normal lifestyle, and the rest will come very easily. I.e look for and learn how to prepare clean foods - e.g. simple chicken, steak, lean ground beef, eggs /egg whites, protein, veggies, potatos, rice, etc. instead of a burger at the fast food joint, Flintstones cereal for breakfast, pizza every night, etc.
)/ 2 - 3 chicken breasts
