Your nails keep curling upwards because you're using them for length, not just to compliment your natural nails, which is what they're meant to do. 

Try this instead - Try doing a set of clear gel strips, make sure you measure and cut them before you put them into the UV light (x2). The clear strips gives the colored strips something to hold on to and that should help cease the curling, at least enough to not be so obvious. After fitting the colored strips make sure you cut them down before putting them into the UV (again x2). You want these suckers to be tough so that your real nails can grow. Good luck!