The situation that you describe is normal. An experienced rider will make the change to the little ring earlier and avoid getting bogged down in the big ring. Likewise, on the downhill side, shift back to the big ring as soon as your cadence starts to get too high. If you ride the same route long enough, you'll know which climbs can be done in the big ring. If the hill is short enough, getting out of the saddle and pedaling standing in the big ring is another option that should get you to the top faster, but it's more tiring.

One downside to a compact crank is the need to shift one more cog after each chainring shift, compared to a standard 53/39. When shifiting to the big ring, expect to shift 2-3 cogs larger (and the opposite when shifting to the little ring). Making a chainring shift without any cog-shifts results in a much too large change in the gear ratio, except on some really sudden changes in slope.