Citation 680 flight crew reported while breaking out of IMC they were cleared visual approach and were above the visual profile and increased their rate of descent resulting in a Terrain GPWS caution. The flight crew returned to the glide path and landed safely at the airport.

Narrative

We requested vectors and a delayed approach into ZZZ because of excessive tailwind for landing RWY XX and smaller thunderstorm cells over ZZZ1 VOR. We quickly got a clearence for a descent from 16000 feet to 13000 feet and a vector for a visual approach to RWY XX when we were approaching ZZZ1. We thought we were going to continue on ATC vectors for additional time to wait out the wind and the thunderstorms but broke out probably around 15000 feet for a straight in visual approach. At that point we were slightly behind the guided visual profile. My partner started to make corrections for an increased descend rate to get on the profile. At some point close to ZZZZZ at approximately 10300 feet we got an TERRAIN GPWS CAUTION annunciation. We continued our level off and very shortly the GPWS extinguished. I took the control of the aircraft and continued with an uneventful approach and landing.Suggestions - It sometimes creates additional workload and attention to accommodate guided visuals in certain situations and locations. It can be frustrating to comply; execute or stay on those recommended profiles when the real world; circumstances and expectations requires different actions. I know they are just that; recommendations but it can become a conflicting consideration.